Bar Graphs and Dot Plots

Save this PDF as:

Size: px
Start display at page:

Transcription

1 CONDENSED L E S S O N 1.1 Bar Graphs and Dot Plots In this lesson you will interpret and create a variety of graphs find some summary values for a data set draw conclusions about a data set based on graphs and summary values This pictograph shows the number of pets of various types that were treated at Uptown Animal Hospital in one week. Specific information, such as the number of pets of each type, is called data. You can often display data in tables and graphs. Pets Treated in One Week Dogs Cats Ferrets Birds Hamsters Lizards 2 pets EXAMPLE Create a table of data and a bar graph from the pictograph above. Solution This table shows the number of pets of each type. Remember that each symbol on the pictograph represents two pets. Pets Treated in One Week Dogs Cats Ferrets Birds Hamsters Lizards The bar graph shows the same data. The height of a bar shows the total in that category, in this case, a particular type of pet. You can use the scale on the vertical axis to measure the height of each bar Dogs Pets Treated in One Week Cats Ferrets Birds Hamsters Lizards Bar graphs gather data into categories, allowing you to quickly compare values for each category. A dot plot shows each item of numerical data above a number line, or horizontal axis. Dot plots make it easy to see gaps and clusters in a data set, as well as how the data spreads along the axis. Investigation: Picturing Pulse Rates This investigation uses data about pulse rates. Pulse rates vary, but a healthy person at rest usually has a pulse rate between certain values. A person with a pulse rate that is too fast or too slow may need medical attention. (continued) 2002 Key Curriculum Press Discovering Algebra Condensed Lessons 11

2 Previous Lesson 1.1 Bar Graphs and Dot Plots (continued) This data set gives pulse rates, in beats per minute, for a group of 30 students For this data set, the minimum (lowest) value is 56 and the maximum (highest) value is 92. The minimum and maximum describe the spread of the data. For example, you could say, The pulse rates are between 56 and 92 bpm. Based only on this data, it appears that a pulse rate of 80 bpm would be normal, while a pulse rate of 36 bpm would be too low. To make a dot plot of the pulse rates, first draw a number line with the minimum value, 56, at the left end. Select a scale and label equal intervals until you reach the maximum value, 92. Minimum pulse rate is 56 bpm. Maximum pulse rate is 92 bpm Every -bpm interval is the same length. For each value in the data set, put a dot above that value on the number line. When a value occurs more than once, stack the dots. For example, the value 6 occurs three times in the data set, so there are three dots above 6. Be sure to label the axis so that it is clear what the data are Pulse rate (bpm) The range of a data set is the difference between the maximum and minimum values. For this data, the range is or 36 bpm. Note that the range does not tell you about the actual values in a data set. If a paramedic tells you that normal pulse rates have a range of 12, this would not tell you anything about the minimum or maximum value or any values in-between. Looking at the dot plot, you can see that there are a few values near the maximum and minimum, but most values cluster between 6 and 80. The value 68 occurs most often, followed by 72. This information gives you an idea of what is a normal pulse for this class, but it could not be used to say what is a normal pulse for all people. Many factors, including age, affect pulse rates. Statistics is a word we use many ways. It is often used to refer to numbers that describe or summarize data. For example, you could collect pulse-rate data from thousands of people and then determine a single value that can be considered normal. This single value can also be called a statistic. 12 Discovering Algebra Condensed Lessons 2002 Key Curriculum Press

3 CONDENSED L E S S O N 1.2 Summarizing Data with Measures of Center Previous In this lesson you will find measures of center for a data set choose the most meaningful measure of center for a situation look at the influence of outliers on the mean of a data set Read the statements at the beginning of the lesson. Each statement uses a single number called a measure of center to describe what is typical about a set of data. The first statement uses the mean, or average. The second statement uses the median, or middle value. The third statement uses the mode, or most frequent value. Investigation: Making Cents of the Center You can use this collection of pennies to help you understand the mean, median, and mode To find the median of the mint years, line up the pennies from oldest to newest. 12 values 12 values The median is the middle value, To find the mode, stack the pennies with the same mint year The mode is the year with the tallest stack, To find the mean, find the sum of the mint years for all the pennies and divide by the number of pennies. sum of mint years mean n umber of pennies 9, You might round the mean up to Here is a dot plot of the mint years with the median, mode, and mean labeled. median mode Mint year mean (continued) 2002 Key Curriculum Press Discovering Algebra Condensed Lessons 13

4 Previous Lesson 1.2 Summarizing Data with Measures of Center (continued) Now enter the penny data into a calculator list, and use your calculator to find the mean and median. (See Calculator Notes 1A and 1B. Refer to Calculator Note 1J to check the settings on your calculator.) Read the descriptions of the measures of center on page 5 of your book. The mean and the median of a set of data may be quite different, and the mode, if it exists, may not be useful. You will need to decide which measure is most meaningful for a given situation. EXAMPLE This data set shows the number of videos rented at a video store each day for 1 days. {5, 75, 2, 68, 9, 53, 5, 63, 5, 70, 65, 68, 71, 60} a. Find the measures of center. b. Which measure best represents the data? Solution a. The mean is about 5 videos. Sum of the data values Because there are an even number of values, the median is the number halfway between the two middle values. In this case, the median is Data values listed in order 2, 5, 9, 53, 5, 5, 60, 63, 65, 68, 68, 70, 71, 75 Number of data values The median is halfway between 60 and 63. This data is bimodal that is, it has two modes, 5 and 68. mean b. To determine which measure best represents the data, look for patterns in the data and consider the shape of the graph. Mode 61.5 Median Mode Videos rented Mean Except for two values (2 and 5), the data are clustered between 9 and 75. The values 2 and 5, called outliers, bring the mean, 5, too far to the left of most of the data values to be the best measure of center. One of the modes is the same as the mean. The other is too high. The median, 61.5, seems to summarize the data best. In the example in your book, the outliers are much greater than the rest of the data. These values pull the mean up. Using the mean to describe data that includes outliers can be misleading. You need to be aware of these limitations when you read advertisements and reports that give measures of center. 1 Discovering Algebra Condensed Lessons 2002 Key Curriculum Press

5 CONDENSED L E S S O N 1.3 Five-Number Summaries and Box Plots Previous In this lesson you will find five-number summaries for data sets interpret and create box plots draw conclusions about a data set based on graphs and summary values use a calculator to make a box plot The table on page 50 of your book shows the total number of points scored by each player on the Chicago Bulls during the NBA season. The five-number summary can give you a good picture of how the Bulls scored as a team. A five-number summary uses five boundary points: the minimum and the maximum, the median (which divides the data in half), the first quartile (the median of the first half), and the third quartile (the median of the second half). The first quartile (Q1), the median, and the third quartile (Q3) divide the data into four equal groups. The example in your book illustrates how to find the five-number summary. A box plot, or box-and-whisker plot, is a visual way to show the five-number summary. This box plot shows the spread of the Bulls scoring data. Notice how the five-number summary is shown in the plot. Even though the four sections of the plot the two whiskers and the two halves of the box are different lengths, each represents 1 of the data. So, for example, the long, right whisker represents the same number of data items as the short, left whisker. Notice that most of the data values are concentrated in the left part of the graph. The long whisker that takes up most of the plot represents only 1 of the values (including Michael Jordan s). Investigation: Pennies in a Box In this investigation, you make a box plot of the penny data from Lesson 1.2. Steps 1 6 First you need to list the values in order and find the five-number summary. Here is some sample data with the minimum, maximum, median, and quartiles labeled. You may want to follow the steps with your data from Lesson 1.2. Minimum First quartile, Q1 Minimum Median Third quartile, Q3 The first quartile is 1986, the median of the first half. Maximum Bulls Points scored First half of data Second half of data Median The third quartile is , the median of the second half. Maximum (continued) 2002 Key Curriculum Press Discovering Algebra Condensed Lessons 15

6 Previous Lesson 1.3 Five-Number Summaries and Box Plots (continued) To make a box plot, draw the horizontal axis (you can use the same scale you used for the dot plot in Lesson 1.2). Draw a short vertical segment just above the median value. Do the same for the first and third quartiles. Then, draw dots over the minimum and maximum values. Min Q1 Med Q3 Max Mint year To finish the plot, draw a box with ends at the first and third quartiles, and draw whiskers extending from the ends of the box to the minimum and maximum values Mint year Compare the box plot with a dot plot of the same data Mint year Both plots show that most of the values are greater than The box plot makes it easier to locate the five-number summary, but, unlike the dot plot, it does not show individual values or how many values there are. If seeing each data value is important, then a box plot is not the best way to display your data. Remember that the four sections of a box plot the two whiskers and the two halves of the box each represent about the same number of data items. The box plot shows that 3 of the mint years are between 1986 and 2000, while only 1 are between 1973 and Steps 7 9 Clear any old data from your calculator and enter the mint years into list L1. Draw a calculator box plot (see Calculator Note 1C). Compare your calculator plot to the one above. If you use the trace function, you can see the five-number summary for the data. Step 10 The difference between the first quartile and the third quartile is the interquartile range, or IQR. Like the range, the interquartile range helps describe the spread in the data. For the sample penny data above, the range is or 27 and the interquartile range is or You can compare two data sets by making two box plots on the same axis. The box plots on page 52 of your book summarize the final test scores for two algebra classes. You can see that Class A has the greater range of scores and the greater IQR. In both classes, half of the students scored above 80. In Class B, all the students scored above 65, whereas in Class A, fewer than three-quarters of the students scored above Discovering Algebra Condensed Lessons 2002 Key Curriculum Press

7 CONDENSED L E S S O N 1. Histograms and Stem-and-Leaf Plots Previous In this lesson you will interpret and create histograms interpret stem-and-leaf plots choose appropriate bin widths for histograms use a calculator to make histograms A dot plot includes a dot for each value in a data set. If a data set contains a large number of values, a dot plot might not be practical. A histogram is related to a dot plot but is more useful when you have a large set of data. Read the information about histograms on page 57 of your book. Notice how the bin width chosen for the histogram affects the appearance of the graph. Investigation: Hand Spans Your hand span is the distance from the tip of your thumb to the tip of your little finger when your fingers are spread. Steps 1 6 Here are hand spans, to the nearest half-centimeter, of students in one algebra class. Hand span To make a histogram of this data, you first need to choose a bin width. As a general rule, try to choose an interval that will give you from 5 to 10 bins. For this data, the range is or 13. If you use a bin width of 2, you will have 7 bins., find the number of data values in each bin. These values are called frequencies. Note that a bin contains the left boundary value, but not the right. So the bin from 17 to 19 includes the values 17, 17.5, 18, and 18.5, but not 19. The value 19 belongs in the bin from 19 to 21. Bin 15 to to to to to to to 29 Frequency Now, draw the axes. Scale the horizontal axis to show hand-span values from 15 to 29 in intervals of 2. Scale the vertical axis to show frequency values from 0 to 8. Finally, draw in bars to show the frequency values in your table. Frequency Hand span (cm) (continued) 2002 Key Curriculum Press Discovering Algebra Condensed Lessons 17

8 Previous Lesson 1. Histograms and Stem-and-Leaf Plots (continued) Steps 7 9 If you enter the hand-span data into list L1 of your calculator, you can experiment with different bin widths. (See Calculator Note 1D for instructions on creating histograms.) Here are histograms of the same data using different bin widths. [15, 29, 1, 0, 5, 1] [15, 29, 1.5, 0, 15, 1] [15, 30, 3, 0, 15, 1] For this data, a bin width of 1.5 or 2 works well. Both bin widths give a nice picture of how the values are distributed, indicating where data values are clustered and where there is a gap in the values. A bin width of 1 shows additional gaps but has a lot of bars. With a bin width of 3, there are too few bars to get a good picture of the distribution, and the gap on the right side is hidden. At right a box plot has been drawn on the same axes as the histogram. Unlike the histogram, the box plot does not show the gap in the data, and it does not give any indication of how many values are in each interval. Frequency Hand span (cm) Like a histogram, a stem plot, or stem-and-leaf plot, groups data values into intervals. However, a stem plot shows each individual data item. For this reason, stem plots are most useful for fairly small data sets. Study the stem plot on page 59 of your book. Make sure you understand how to read the values. The example on page 60 of your book shows how to use the data in a stem plot to create a histogram. The values in the stem plot are years. The stem values show the first three digits of the year, and the leaves show the last digit. So, for example, the values next to the stem 18 represent the years 180, 181, 183, and 188. Read through the example to see how the histogram was created. Then, enter the data into your calculator and experiment with different bin widths. Here are some possibilities. Think about which bin widths best show the spread and distribution of the values. 18 Discovering Algebra Condensed Lessons 2002 Key Curriculum Press

9 CONDENSED L E S S O N 1.6 Two-Variable Data Previous In this lesson you will practice plotting points on the coordinate plane create a scatter plot look for a relationship between two variables based on a graph use your calculator to create a scatter plot A variable is a quantity such as pulse rate or mint year whose value can vary. So far in this chapter, you have been working with one-variable data. You have used dot plots, box plots, histograms, and stem plots to display one-variable data. It is often interesting to look at information about two variables to try to discover a relationship. For example, you could collect data about height and shoe size to see if taller people tend to have larger feet than shorter people. Making a scatter plot is a good way to look for a relationship in two-variable data. Read the information about two-variable graphs on page 67 of your book. Investigation: Backed into a Corner This investigation involves collecting and graphing two-variable data. Steps 1 To collect the data, tape two rulers to a desk so that they form an angle., measure the diameter of a circular object. Then, place the object between the rulers so that it fits snuggly, and measure the distance from the vertex of the angle to the point where the object touches the ruler. Distance from vertex Here are some sample data for this activity. Diameter (cm) Distance from vertex (cm) Steps 5 7 To see if there might be a relationship between the variables diameter and distance from vertex, you can make a scatter plot. Before plotting the data, you need to set up and scale the axes to accommodate all the values. You can put either variable on either axis. In the graph on the following page, the diameter values are on the x-axis and the distance-from-vertex values are on the y-axis. The greatest diameter value is 7.3, and the greatest distance-from-vertex value is If you let each grid unit on the x-axis represent 0.5 cm and each grid unit on the y-axis represent 1 cm, all the values will fit on a 16-by-16 grid. Be sure to label the axes with the names of the variables. (continued) 2002 Key Curriculum Press Discovering Algebra Condensed Lessons 19

10 Previous Lesson 1.6 Two-Variable Data (continued) To plot the data, think of each row as an ordered pair. For example, to graph the first row of values, plot (.6, 9.6) by moving along the horizontal axis to.6 and then straight up until you are even with 9.6. On the right below is the completed scatter plot. y y Distance from vertex (cm) (.6, 9.6) Distance from vertex (cm) (7.3, 15.7) (6.7, 1.2) (5.5, 11.5) (.6, 9.6) (.0, 8.8) (3.1, 6.) (2., 5.) (1.9, 3.7) Diameter (cm) x Diameter (cm) x Steps 8 9 Notice that the points form a straight-line pattern. The graph indicates that the greater the diameter of an object, the greater its distance from the vertex will be. To make a scatter plot on your calculator, you need to enter the data into two lists. Try making a scatter plot of the data above on your calculator. (See Calculator Note 1E to learn how to make a scatter plot.) Review the example on page 69 of your book. The graph in the example, like the graph created in the investigation, is a first-quadrant graph because all the values are positive. Sometimes data includes negative values and requires more than one quadrant. EXAMPLE Solution If you write checks for more money than you have in your account, the account will have a negative balance. The graph at right shows the balance in a checking account at the end of each day over a five-day period. Describe the balance each day. The point (1, 150) shows that on the first day, the balance was \$150. The point (2, 50) shows that on the second day, the balance was \$50. The points (3, 350) and (, 350) indicate that on the third and fourth days, the balance was \$350. The point (5, 200) means that on the fifth day, the balance was \$200. Balance (dollars) y (1, 150) 1 (2, 50) (3, 350) (, 350) 3 5 Day (5, 200) x 20 Discovering Algebra Condensed Lessons 2002 Key Curriculum Press

11 CONDENSED L E S S O N 1.7 Estimating Previous In this lesson you will practice your estimation skills create a scatter plot draw conclusions about a data set based on graphs use your calculator to create a scatter plot In this lesson you see how to use a scatter plot to compare estimated values to actual values. Investigation: Guesstimating Steps 1 3 To test your estimation skills, you can estimate the distances from a starting point to several objects and then measure to find the actual distances. This table shows some sample data. You may want to collect and use your own data, or just add a few of your own values to this table. Actual distance Estimated distance Description (m), x (m), y Ted s desk Zoe s desk Chalkboard Teacher s desk Blue floor tile Corner of classroom Garbage can Jing s pencil Bookshelf Steps 5 You can make a scatter plot to compare the estimated distances with the actual distances. First, set up the axes. Put the actual distances on the x-axis and the estimated distances on the y-axis. Use the same scale on both axes. Plot a point for each pair of values in the table, using the actual distance for the x-value and the estimated distance for the y-value. For example, plot (.32, 3.80) to represent the data for the chalkboard. Here is the completed graph. Think about what the graph would look like if all of the estimates had been the same as the actual measurements. That is, imagine that the graph included (1.86, 1.86), (1.56, 1.56), (.32,.32), and so on. In this case, the points would fall on a straight line. Estimated distance (m) 5 3 y (.87,.50) (3.87,.25) (.32, 3.80) (2.35, 2.75) 2 (1.85, 2.00) (1.86, 1.75) (1.50, 1.50) 1 (0.57, 0.50) (0.29, 0.25) Actual distance (m) x (continued) 2002 Key Curriculum Press Discovering Algebra Condensed Lessons 21

12 Previous Lesson 1.7 Estimating (continued) Steps 6 9 Use your graphing calculator to make a scatter plot of the data. Here s what the plot will look like if you use the same scale used in the preceding graph: The line y x represents all the points for which the y-value equals the x-value. In this case, it represents all the points for which the estimated distance equals the actual distance. Graph the line y x in the same window as your scatter plot. (See Calculator Note 1H to graph a scatter plot and an equation simultaneously.) Points that are closer to the line represent better estimates than points that are farther from the line. Use the trace function to look at the coordinates of the points. Notice that points for which the estimate is too low fall below the line and that points for which the estimate is too high fall above the line. y Estimated distance (m) (1.50, 1.50) Estimate is too high (2.35, 2.75) (1.85, 2.00) (0.57, 0.50) (0.29, 0.25) (.87,.50) (3.87,.25) y = x (1.86, 1.75) Estimate is the same as the actual value Estimate is too low (.32, 3.80) Actual distance (m) x 22 Discovering Algebra Condensed Lessons 2002 Key Curriculum Press

14 Previous Lesson 1.8 Using Matrices to Organize and Combine Data (continued) Steps 13 The row matrix [A] and the column matrix [B] contain all the information you need to calculate the total food cost at Pizza Palace. Matrix [A] shows the item quantities, and matrix [B] shows the costs [A] [ 5 10] [B] 3.35 Enter [A] and [B] into your calculator and find their product, [A] [B], or 11.0 [ 5 10] (See Calculator Note 1P to learn how to multiply two matrices.) You should get the 1 1 matrix [83.85]. The matrix entry, 83.85, is the total price calculated above. The calculator multiplies each entry in the row matrix by the corresponding entry in the column matrix and adds the results. This is the same calculation [ 5 10] 3.35 [ ] [83.85] 2.15 You can find the total cost of the food items at Tony s Pizzeria by multiplying the matrices below. Multiply the matrices on your calculator. You should get [85.90] [ 5 10] You can do one matrix calculation to find the total cost for both restaurants [ 5 10] Do this calculation on your calculator. You should get the 2 1 matrix [ ]. To get the first entry in the product, the calculator multiplies the row matrix by the first column. To get the second entry, the calculator multiplies the row matrix by the second column. If you try to multiply the matrices in the reverse order, you will get an error message. To multiply two matrices, the number of columns in the first matrix must be the same as the number of columns in the second because each column entry in the first matrix is multiplied by the corresponding row entry in the second matrix. Work through Example C in your book to get more practice multiplying matrices. 2 Discovering Algebra Condensed Lessons 2002 Key Curriculum Press

The right edge of the box is the third quartile, Q 3, which is the median of the data values above the median. Maximum Median

CONDENSED LESSON 2.1 Box Plots In this lesson you will create and interpret box plots for sets of data use the interquartile range (IQR) to identify potential outliers and graph them on a modified box

Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs

Types of Variables Chapter 1: Looking at Data Section 1.1: Displaying Distributions with Graphs Quantitative (numerical)variables: take numerical values for which arithmetic operations make sense (addition/averaging)

Exercise 1.12 (Pg. 22-23)

Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

AP * Statistics Review. Descriptive Statistics

AP * Statistics Review Descriptive Statistics Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production

Exploratory data analysis (Chapter 2) Fall 2011

Exploratory data analysis (Chapter 2) Fall 2011 Data Examples Example 1: Survey Data 1 Data collected from a Stat 371 class in Fall 2005 2 They answered questions about their: gender, major, year in school,

Box-and-Whisker Plots

Learning Standards HSS-ID.A. HSS-ID.A.3 3 9 23 62 3 COMMON CORE.2 Numbers of First Cousins 0 3 9 3 45 24 8 0 3 3 6 8 32 8 0 5 4 Box-and-Whisker Plots Essential Question How can you use a box-and-whisker

Common Tools for Displaying and Communicating Data for Process Improvement

Common Tools for Displaying and Communicating Data for Process Improvement Packet includes: Tool Use Page # Box and Whisker Plot Check Sheet Control Chart Histogram Pareto Diagram Run Chart Scatter Plot

DesCartes (Combined) Subject: Mathematics Goal: Statistics and Probability

DesCartes (Combined) Subject: Mathematics Goal: Statistics and Probability RIT Score Range: Below 171 Below 171 Data Analysis and Statistics Solves simple problems based on data from tables* Compares

Descriptive Statistics

Y520 Robert S Michael Goal: Learn to calculate indicators and construct graphs that summarize and describe a large quantity of values. Using the textbook readings and other resources listed on the web

STATS8: Introduction to Biostatistics. Data Exploration. Babak Shahbaba Department of Statistics, UCI

STATS8: Introduction to Biostatistics Data Exploration Babak Shahbaba Department of Statistics, UCI Introduction After clearly defining the scientific problem, selecting a set of representative members

Describing, Exploring, and Comparing Data

24 Chapter 2. Describing, Exploring, and Comparing Data Chapter 2. Describing, Exploring, and Comparing Data There are many tools used in Statistics to visualize, summarize, and describe data. This chapter

Session 7 Bivariate Data and Analysis

Session 7 Bivariate Data and Analysis Key Terms for This Session Previously Introduced mean standard deviation New in This Session association bivariate analysis contingency table co-variation least squares

HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

Mathematics Revision Guides Histograms, Cumulative Frequency and Box Plots Page 1 of 25 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier HISTOGRAMS, CUMULATIVE FREQUENCY AND BOX PLOTS

Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 6 8

Ma KEY STAGE 3 Mathematics test TIER 6 8 Paper 1 Calculator not allowed First name Last name School 2009 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You

Diagrams and Graphs of Statistical Data

Diagrams and Graphs of Statistical Data One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in

Valor Christian High School Mrs. Bogar Biology Graphing Fun with a Paper Towel Lab

1 Valor Christian High School Mrs. Bogar Biology Graphing Fun with a Paper Towel Lab I m sure you ve wondered about the absorbency of paper towel brands as you ve quickly tried to mop up spilled soda from

OA3-10 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20

Level 1 - Maths Targets TARGETS. With support, I can show my work using objects or pictures 12. I can order numbers to 10 3

Ma Data Hling: Interpreting Processing representing Ma Shape, space measures: position shape Written Mental method s Operations relationship s between them Fractio ns Number s the Ma1 Using Str Levels

Summarizing and Displaying Categorical Data

Summarizing and Displaying Categorical Data Categorical data can be summarized in a frequency distribution which counts the number of cases, or frequency, that fall into each category, or a relative frequency

MD5-26 Stacking Blocks Pages 115 116

MD5-26 Stacking Blocks Pages 115 116 STANDARDS 5.MD.C.4 Goals Students will find the number of cubes in a rectangular stack and develop the formula length width height for the number of cubes in a stack.

Descriptive statistics Statistical inference statistical inference, statistical induction and inferential statistics

Descriptive statistics is the discipline of quantitatively describing the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics (or inductive statistics),

In A Heartbeat (Algebra)

The Middle School Math Project In A Heartbeat (Algebra) Objective Students will apply their knowledge of scatter plots to discover the correlation between heartbeats per minute before and after aerobic

Box Plots. Objectives To create, read, and interpret box plots; and to find the interquartile range of a data set. Family Letters

Bo Plots Objectives To create, read, and interpret bo plots; and to find the interquartile range of a data set. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop

Three daily lessons. Year 5

Unit 6 Perimeter, co-ordinates Three daily lessons Year 4 Autumn term Unit Objectives Year 4 Measure and calculate the perimeter of rectangles and other Page 96 simple shapes using standard units. Suggest

Statistics Revision Sheet Question 6 of Paper 2

Statistics Revision Sheet Question 6 of Paper The Statistics question is concerned mainly with the following terms. The Mean and the Median and are two ways of measuring the average. sumof values no. of

Measurement with Ratios

Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve real-world and mathematical

OREGON FOCUS ON MATH OAKS HOT TOPICS TEST PREPARATION WORKBOOK 200-204 8 th Grade TO BE USED AS A SUPPLEMENT FOR THE OREGON FOCUS ON MATH MIDDLE SCHOOL CURRICULUM FOR THE 200-204 SCHOOL YEARS WHEN THE

Data Exploration Data Visualization

Data Exploration Data Visualization What is data exploration? A preliminary exploration of the data to better understand its characteristics. Key motivations of data exploration include Helping to select

Unit 13 Handling data. Year 4. Five daily lessons. Autumn term. Unit Objectives. Link Objectives

Unit 13 Handling data Five daily lessons Year 4 Autumn term (Key objectives in bold) Unit Objectives Year 4 Solve a problem by collecting quickly, organising, Pages 114-117 representing and interpreting

Box-and-Whisker Plots

Mathematics Box-and-Whisker Plots About this Lesson This is a foundational lesson for box-and-whisker plots (boxplots), a graphical tool used throughout statistics for displaying data. During the lesson,

Scope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B

Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced

Grade 6 Mathematics Assessment. Eligible Texas Essential Knowledge and Skills

Grade 6 Mathematics Assessment Eligible Texas Essential Knowledge and Skills STAAR Grade 6 Mathematics Assessment Mathematical Process Standards These student expectations will not be listed under a separate

Shape of Data Distributions

Lesson 13 Main Idea Describe a data distribution by its center, spread, and overall shape. Relate the choice of center and spread to the shape of the distribution. New Vocabulary distribution symmetric

Comparing Sets of Data Grade Eight

Ohio Standards Connection: Data Analysis and Probability Benchmark C Compare the characteristics of the mean, median, and mode for a given set of data, and explain which measure of center best represents

Lesson 4: Solving and Graphing Linear Equations

Lesson 4: Solving and Graphing Linear Equations Selected Content Standards Benchmarks Addressed: A-2-M Modeling and developing methods for solving equations and inequalities (e.g., using charts, graphs,

Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 5 7

Ma KEY STAGE 3 Mathematics test TIER 5 7 Paper 1 Calculator not allowed First name Last name School 2009 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You

Grade 6 Mathematics Performance Level Descriptors

Limited Grade 6 Mathematics Performance Level Descriptors A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Grade 6 Mathematics. A student at this

Bellwork Students will review their study guide for their test. Box-and-Whisker Plots will be discussed after the test.

Course: 7 th Grade Math Student Objective (Obj. 5c) TSW graph and interpret data in a box-and-whisker plot. DETAIL LESSON PLAN Friday, March 23 / Monday, March 26 Lesson 1-10 Box-and-Whisker Plot (Textbook

6.4 Normal Distribution

Contents 6.4 Normal Distribution....................... 381 6.4.1 Characteristics of the Normal Distribution....... 381 6.4.2 The Standardized Normal Distribution......... 385 6.4.3 Meaning of Areas under

Chapter 2: Frequency Distributions and Graphs

Chapter 2: Frequency Distributions and Graphs Learning Objectives Upon completion of Chapter 2, you will be able to: Organize the data into a table or chart (called a frequency distribution) Construct

Discovering Math: Using and Collecting Data Teacher s Guide

Teacher s Guide Grade Level: 3-5 Curriculum Focus: Mathematics Lesson Duration: Four class periods Program Description Discovering Math: Using and Collecting Data From data points and determining spread

HSPA 10 CSI Investigation Height and Foot Length: An Exercise in Graphing

HSPA 10 CSI Investigation Height and Foot Length: An Exercise in Graphing In this activity, you will play the role of crime scene investigator. The remains of two individuals have recently been found trapped

Math Journal HMH Mega Math. itools Number

Lesson 1.1 Algebra Number Patterns CC.3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. Identify and

Variables. Exploratory Data Analysis

Exploratory Data Analysis Exploratory Data Analysis involves both graphical displays of data and numerical summaries of data. A common situation is for a data set to be represented as a matrix. There is

Part 1: Background - Graphing

Department of Physics and Geology Graphing Astronomy 1401 Equipment Needed Qty Computer with Data Studio Software 1 1.1 Graphing Part 1: Background - Graphing In science it is very important to find and

DesCartes (Combined) Subject: Mathematics Goal: Data Analysis, Statistics, and Probability

DesCartes (Combined) Subject: Mathematics Goal: Data Analysis, Statistics, and Probability RIT Score Range: Below 171 Below 171 171-180 Data Analysis and Statistics Data Analysis and Statistics Solves

Bar Graphs with Intervals Grade Three

Bar Graphs with Intervals Grade Three Ohio Standards Connection Data Analysis and Probability Benchmark D Read, interpret and construct graphs in which icons represent more than a single unit or intervals

Lesson 2: Constructing Line Graphs and Bar Graphs

Lesson 2: Constructing Line Graphs and Bar Graphs Selected Content Standards Benchmarks Assessed: D.1 Designing and conducting statistical experiments that involve the collection, representation, and analysis

Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c

Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics

Mathematical goals. Starting points. Materials required. Time needed

Level S6 of challenge: B/C S6 Interpreting frequency graphs, cumulative cumulative frequency frequency graphs, graphs, box and box whisker and plots whisker plots Mathematical goals Starting points Materials

Basic Understandings

Activity: TEKS: Exploring Transformations Basic understandings. (5) Tools for geometric thinking. Techniques for working with spatial figures and their properties are essential to understanding underlying

Integers (pages 294 298)

A Integers (pages 294 298) An integer is any number from this set of the whole numbers and their opposites: { 3, 2,, 0,, 2, 3, }. Integers that are greater than zero are positive integers. You can write

Interpreting Data in Normal Distributions

Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,

2 Describing, Exploring, and

2 Describing, Exploring, and Comparing Data This chapter introduces the graphical plotting and summary statistics capabilities of the TI- 83 Plus. First row keys like \ R (67\$73/276 are used to obtain

Big Ideas in Mathematics

Big Ideas in Mathematics which are important to all mathematics learning. (Adapted from the NCTM Curriculum Focal Points, 2006) The Mathematics Big Ideas are organized using the PA Mathematics Standards

Data Visualization Techniques

Data Visualization Techniques From Basics to Big Data with SAS Visual Analytics WHITE PAPER SAS White Paper Table of Contents Introduction.... 1 Generating the Best Visualizations for Your Data... 2 The

Elements of a graph. Click on the links below to jump directly to the relevant section

Click on the links below to jump directly to the relevant section Elements of a graph Linear equations and their graphs What is slope? Slope and y-intercept in the equation of a line Comparing lines on

Vocabulary Cards and Word Walls Revised: June 29, 2011

Vocabulary Cards and Word Walls Revised: June 29, 2011 Important Notes for Teachers: The vocabulary cards in this file match the Common Core, the math curriculum adopted by the Utah State Board of Education,

Algebra 2 Chapter 1 Vocabulary. identity - A statement that equates two equivalent expressions.

Chapter 1 Vocabulary identity - A statement that equates two equivalent expressions. verbal model- A word equation that represents a real-life problem. algebraic expression - An expression with variables.

Problem 1 The Parabola Examine the data in L 1 and L to the right. Let L 1 be the x- value and L be the y-values for a graph. 1. How are the x and y-values related? What pattern do you see? To enter the

Statistics and Probability

Statistics and Probability TABLE OF CONTENTS 1 Posing Questions and Gathering Data. 2 2 Representing Data. 7 3 Interpreting and Evaluating Data 13 4 Exploring Probability..17 5 Games of Chance 20 6 Ideas

LESSON TITLE: Math in Restaurants (by Deborah L. Ives, Ed.D)

LESSON TITLE: Math in Restaurants (by Deborah L. Ives, Ed.D) GRADE LEVEL/COURSE: Grades 7-10 Algebra TIME ALLOTMENT: Two 45-minute class periods OVERVIEW Using video segments and web interactives from

The Circumference Function

2 Geometry You have permission to make copies of this document for your classroom use only. You may not distribute, copy or otherwise reproduce any part of this document or the lessons contained herein

Graph it! Grade Six. Estimated Duration: Three hours

Ohio Standards Connection Data Analysis and Probability Benchmark A Read, Create and use line graphs, histograms, circle graphs, box-and whisker plots, stem-and-leaf plots, and other representations when

DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

Unit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas:

Unit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas: Developing strategies for determining the zeroes of quadratic functions Making connections between the meaning

MATHEMATICS TEST. Paper 1 calculator not allowed LEVEL 6 TESTS ANSWER BOOKLET. First name. Middle name. Last name. Date of birth Day Month Year

LEVEL 6 TESTS ANSWER BOOKLET Ma MATHEMATICS TEST LEVEL 6 TESTS Paper 1 calculator not allowed First name Middle name Last name Date of birth Day Month Year Please circle one Boy Girl Year group School

Parallel and Perpendicular. We show a small box in one of the angles to show that the lines are perpendicular.

CONDENSED L E S S O N. Parallel and Perpendicular In this lesson you will learn the meaning of parallel and perpendicular discover how the slopes of parallel and perpendicular lines are related use slopes

Interpret Box-and-Whisker Plots. Make a box-and-whisker plot

13.8 Interpret Box-and-Whisker Plots Before You made stem-and-leaf plots and histograms. Now You will make and interpret box-and-whisker plots. Why? So you can compare sets of scientific data, as in Ex.

Data Mining: Exploring Data. Lecture Notes for Chapter 3. Introduction to Data Mining

Data Mining: Exploring Data Lecture Notes for Chapter 3 Introduction to Data Mining by Tan, Steinbach, Kumar What is data exploration? A preliminary exploration of the data to better understand its characteristics.

Students summarize a data set using box plots, the median, and the interquartile range. Students use box plots to compare two data distributions.

Student Outcomes Students summarize a data set using box plots, the median, and the interquartile range. Students use box plots to compare two data distributions. Lesson Notes The activities in this lesson

Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering

Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques

Excel -- Creating Charts

Excel -- Creating Charts The saying goes, A picture is worth a thousand words, and so true. Professional looking charts give visual enhancement to your statistics, fiscal reports or presentation. Excel

Indicator 2: Use a variety of algebraic concepts and methods to solve equations and inequalities.

3 rd Grade Math Learning Targets Algebra: Indicator 1: Use procedures to transform algebraic expressions. 3.A.1.1. Students are able to explain the relationship between repeated addition and multiplication.

Year 9 mathematics test

Ma KEY STAGE 3 Year 9 mathematics test Tier 5 7 Paper 1 Calculator not allowed First name Last name Class Date Please read this page, but do not open your booklet until your teacher tells you to start.

Decimals and Percentages

Decimals and Percentages Specimen Worksheets for Selected Aspects Paul Harling b recognise the number relationship between coordinates in the first quadrant of related points Key Stage 2 (AT2) on a line

GeoGebra. 10 lessons. Gerrit Stols

GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter

Warm-Up Oct. 22. Daily Agenda:

Evaluate y = 2x 3x + 5 when x = 1, 0, and 2. Daily Agenda: Grade Assignment Go over Ch 3 Test; Retakes must be done by next Tuesday 5.1 notes / assignment Graphing Quadratic Functions 5.2 notes / assignment

Prentice Hall Mathematics: Course 1 2008 Correlated to: Arizona Academic Standards for Mathematics (Grades 6)

PO 1. Express fractions as ratios, comparing two whole numbers (e.g., ¾ is equivalent to 3:4 and 3 to 4). Strand 1: Number Sense and Operations Every student should understand and use all concepts and

Polynomial Degree and Finite Differences

CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson you will learn the terminology associated with polynomials use the finite differences method to determine the degree of a polynomial

A Correlation of to the Minnesota Academic Standards Grades K-6 G/M-204 Introduction This document demonstrates the high degree of success students will achieve when using Scott Foresman Addison Wesley

Chapter 1: Exploring Data

Chapter 1: Exploring Data Chapter 1 Review 1. As part of survey of college students a researcher is interested in the variable class standing. She records a 1 if the student is a freshman, a 2 if the student

Unit 6 Direction and angle

Unit 6 Direction and angle Three daily lessons Year 4 Spring term Unit Objectives Year 4 Recognise positions and directions: e.g. describe and find the Page 108 position of a point on a grid of squares

CAMI Education linked to CAPS: Mathematics

- 1 - TOPIC 1.1 Whole numbers _CAPS curriculum TERM 1 CONTENT Mental calculations Revise: Multiplication of whole numbers to at least 12 12 Ordering and comparing whole numbers Revise prime numbers to

Vertical Alignment Colorado Academic Standards 6 th - 7 th - 8 th

Vertical Alignment Colorado Academic Standards 6 th - 7 th - 8 th Standard 3: Data Analysis, Statistics, and Probability 6 th Prepared Graduates: 1. Solve problems and make decisions that depend on un

GeoGebra Statistics and Probability

GeoGebra Statistics and Probability Project Maths Development Team 2013 www.projectmaths.ie Page 1 of 24 Index Activity Topic Page 1 Introduction GeoGebra Statistics 3 2 To calculate the Sum, Mean, Count,

Using SPSS, Chapter 2: Descriptive Statistics

1 Using SPSS, Chapter 2: Descriptive Statistics Chapters 2.1 & 2.2 Descriptive Statistics 2 Mean, Standard Deviation, Variance, Range, Minimum, Maximum 2 Mean, Median, Mode, Standard Deviation, Variance,

Creating Charts in Microsoft Excel A supplement to Chapter 5 of Quantitative Approaches in Business Studies

Creating Charts in Microsoft Excel A supplement to Chapter 5 of Quantitative Approaches in Business Studies Components of a Chart 1 Chart types 2 Data tables 4 The Chart Wizard 5 Column Charts 7 Line charts

Paper 2. Year 9 mathematics test. Calculator allowed. Remember: First name. Last name. Class. Date

Ma KEY STAGE 3 Year 9 mathematics test Tier 6 8 Paper 2 Calculator allowed First name Last name Class Date Please read this page, but do not open your booklet until your teacher tells you to start. Write

CRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide

Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are

5/31/2013. 6.1 Normal Distributions. Normal Distributions. Chapter 6. Distribution. The Normal Distribution. Outline. Objectives.

The Normal Distribution C H 6A P T E R The Normal Distribution Outline 6 1 6 2 Applications of the Normal Distribution 6 3 The Central Limit Theorem 6 4 The Normal Approximation to the Binomial Distribution

In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data.

MATHEMATICS: THE LEVEL DESCRIPTIONS In mathematics, there are four attainment targets: using and applying mathematics; number and algebra; shape, space and measures, and handling data. Attainment target

Paper 1. Calculator not allowed. Mathematics test. First name. Last name. School. Remember KEY STAGE 3 TIER 4 6

Ma KEY STAGE 3 Mathematics test TIER 4 6 Paper 1 Calculator not allowed First name Last name School 2007 Remember The test is 1 hour long. You must not use a calculator for any question in this test. You

Data Visualization Techniques

Data Visualization Techniques From Basics to Big Data with SAS Visual Analytics WHITE PAPER SAS White Paper Table of Contents Introduction.... 1 Generating the Best Visualizations for Your Data... 2 The

Standard 1: Students can understand and apply a variety of math concepts.

Grade Level: 4th Teacher: Pelzer/Reynolds Math Standard/Benchmark: A. understand and apply number properties and operations. Grade Level Objective: 1.A.4.1: develop an understanding of addition, subtraction,

Iris Sample Data Set. Basic Visualization Techniques: Charts, Graphs and Maps. Summary Statistics. Frequency and Mode

Iris Sample Data Set Basic Visualization Techniques: Charts, Graphs and Maps CS598 Information Visualization Spring 2010 Many of the exploratory data techniques are illustrated with the Iris Plant data

Unit 7: Normal Curves

Unit 7: Normal Curves Summary of Video Histograms of completely unrelated data often exhibit similar shapes. To focus on the overall shape of a distribution and to avoid being distracted by the irregularities

Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material