Ch 2 ( Practice Problems)

Transcription

1 Ch 2 ( Practice Problems) Practice 1 (Qualitative Data) The following data gives the results of a sample survey. The survey asked the participants whether they liked a specific brand of coffee or not. Letters Y, N and D represent the 3 categories of answers (Yes, No, Don t know). D N N Y Y Y N Y D N Y Y Y Y N Y Y N N Y N Y Y N D N Y N Y Y Y Y N N Y Y N N D Y a) Prepare the frequency distribution table and calculate the relative frequency and percentage frequency for all the categories. CATEGORY FREQUENCY RELATIVE FREQ = f f % FREQ yes 21 21/40 = no don t know Total 100% Note: The symbol represents a sum of values. b) What percent of elements belong to the Y category? c) What percent of elements belong to the N or D? Practice 2 The 2000 Census results include a summary of the racial composition of the population. The races reported by the populations of the United States and the State of California are summarized below. The data are given in millions. (Source: census.gov) Category (Race) Frequency Relative Frequency White Black Asian American Indian Pacific Islands Other single race Two or more races /281.5= Total = a) Construct a relative frequency distribution for races in the U.S. b) What percentage of U.S. residents claims two or more races? 1

2 Practice 3 (Quantitative Data) Numbers of keyboards assembled in a 20th Century Electronic Company for a sample of 25 days are as follows: (n = 25) Prepare a Frequency Distribution Table with 5 classes. Step 1) Calculate the class width. Class Class is an interval including all the values that fall within two numbers. Class represents a variable and has lower and upper limits. Class Width (size) Range(Hi-Low) Width= Number of classes Round up if necessary. Class width is also the difference between two consecutive lower class limits. (normally from 5-20) Step 2) Choose either the minimum data value or a convenient value below the minimum data values the first lower class limit. Lower Class Limits The smallest numbers that can belong to the different classes. Step 3) Using the first lower class limit and the class width, list the other lower class limits. (Hint: Add the class width to the first lower class limit to get the second lower class limit, and so on.) List the lower class limits in a vertical column and then enter the upper class limits. Upper Class Limits The largest numbers that can belong to the different classes. Step 4) Find the total frequency Frequency Distribution Number of Keyboards Frequency (f) Relative Frequency (rf) Class Boundaries The numbers used to separate the classes, but without the gaps created by class limits. (which are used to draw a histogram) Class Midpoint (mark) Lower Limit + Upper Limit 2 2

3 Cumulative Frequency Distribution Table It lists all the classes and the sum of the frequencies of each class and all previous classes. (Gives total number of values that fall below the upper boundary of each class) Cumulative Frequency Distribution Number of Keyboards Cumulative Frequency (cf) Practice 4 (Quantitative Data) The following frequency table represents the employment information on Alpha Corporation. Classes (Years of service) Frequency (No. of employees) a) Find the sample size. b) Find the number of classes. c) Find the class width. d) Find the midpoint of each class. Practice 5: The following frequency distribution is the weekly earning for a sample of 100 employees selected from a large company. a) Find the class width. b) Find the - lower class limits: - upper class limits: c) Find the class boundariy of the second class. d) Find the class midpoint of the third class. e) Find the relative and percent frequencies. f) What percent of the employees earned $650 or more per week? Classes (Weekly Earnings) midpoint Frequency (No. of employees) Relative Frequency Percent Frequency 3

4 Cumulative Frequency Distribution Table It lists all the classes and the sum of the frequencies of each class and all previous classes. (Gives total number of values that fall below the upper boundary of each class) Practice 6: Construct the cumulative frequency distribution that corresponds to the given frequency distribution. Height (inches) midpoint Frequency Cumulative Frequency Practice 7: Find the cumulative frequency for Practice problem 5 (add the column to the right). Practice 8: Histograms: Construct a histogram for Practice 6 Practice 9: Normal Distribution Determine the type of distribution for practice 6, using the histogram that you made. 4

5 2 4 Statistical Graphics *Graphs for (for Quantitative Data) Frequency Polygon A frequency polygon uses like segments connected to points directly above class midpoint values. Make a class before the 1 st midpoint and after the last one and connect all the midpoint values of all classes with line segments. The Vertical axis is the frequency. CA A) Construct a frequency polygon for Problem 6 Ogive A line graph that represents cumulative frequencies. Draw the graph by joining with straight lines the dots marked above the upper boundaries of classes at height equal to their cumulative frequencies. CA B) Create the ogive chart for prob. 6 5

6 Stem and Leaf Plots A Stem and Leaf plot represents data by separating each value into 2 parts; the stem (such as the leftmost digit) and the leaf (such as the rightmost digit). Note that the leaves are arranges in increasing order. Example 1: Construct a stem-and-leaf plot: 23, 54, 32, 50, 33, 42, 54, 25, 28, 31, 20, 60, 75, 81, 76, 62, 61, 51 C. Create a frequency chart with 5 classes for the data in example 10: 6

7 Dotplots A dot plot is drawn by placing each observation horizontally in increasing order and placing a dot above the observation each time it is observed. Example 2: The following data represent the number of available cars in a household based on a random sample of 50 households. Draw a dot plot of the data Data based on results reported by the United States Bureau of the Census. Graphs for (for Qualitative Data) Bar Graphs Uses bars of equal width to show frequencies of categories of qualitative data. Vertical scale represents frequencies or relative frequencies. Horizontal scale identifies the different categories of qualitative data. D. What percentage of college students gets their information from television? A multiple bar graph has two or more sets of bars, and is used to compare two or more data sets. E. In what year is the male median income about twice that of the female median income. 7

8 Pareto Charts A bar graph for qualitative data, with the bars arranges in order according to frequencies. F. How do you think arranging the bars in order of frequency can influence the readers of the chart? Pie Charts A graph depicting qualitative data as slices of a circle, size of slice is proportional to frequency count. Apartments 35% Single family 39% Condo 18% Townhouse 6% Duplex 2% G. The pie chart below shows the percent of the total population of 12,200 of Springfield living in the given types of housing. Find the number of people who live in single family housing (round to nearest whole number.) 8

9 Scatter Plots A plot of paired (x,y) data with a horizontal x-axis and a vertical y-axis. Used to determine whether there is a relationship between the two variables. H. Just looking at the graph, does there appear to be a linear correlation between chirps per minute and temperature? Explain. Time Series Graph: Data that have been collected at different points in time: time-series data I. List some things you should remember from this chapter: 9