Statistics 101 Homework 2

Size: px

Start display at page:

Download "Statistics 101 Homework 2"

Angelica Horton
7 years ago
Views:

1 Statistics 101 Homework 2 Solution Reading: January 23 January 25 Chapter 4 January 28 Chapter 5 Assignment: 1. As part of a physiology study participants had their heart rate (beats per minute) taken by a trained nurse practitioner. Below are heart rates for a sample of 20 females a) Answer the questions, Who? What? for these data. Who? Females. What? Heart rate (beats per minute). b) Make a stem-and-leaf display of the females heart rates (use a split stem) * 7 5* * * * * c) Using the stem-and-leaf display, describe the distribution of heart rates for females. Make sure you mention the shape, center, spread and any outliers or other interesting characteristics of the distribution. The shape is mounded on the high side (on the right) and skewed towards lower values (to the left). The center is in the low 70 s beats per minute. The spread is from 57 to 79 beats per minute. There are no apparent outliers or other unusual characteristics. d) Calculate the sample mean heart rate. The sample mean heart rate is beats per minute. 1

2 e) Calculate the sample median heart rate. Why is the sample mean heart rate lower than the sample median heart rate? The sample median heart rate is 71.5 beats per minute. The sample mean is lower than the sample median because the distribution is skewed to the left and the sample mean tends to be pulled in the direction of the skew. f) Calculate the five number summary for these data. minimum: 57.0 bpm lower quartile: 68.0 bpm median: 71.5 bpm upper quartile: 75.5 bpm maximum: 79.0 bpm g) Given the value ( y y) 2 for these data s = = = 6.0 beats per minute 19 = , calculate the sample standard deviation h) Which do you think provides a more informative summary of these data; a five number summary or the sample mean and sample standard deviation? Briefly explain your answer. The shape of the distribution is skewed left. A five number summary would be a more informative summary. The heart rates for a sample of 20 males were also taken. i) Describe the distribution of heart rates for males. Make sure you mention the shape, center, spread and any outliers or other interesting characteristics of the distribution. The shape of the distribution is symmetric and mounded in the middle. The center is between 70 and 75 beats per minute. The spread is from 64 to 82 beats per minute. There are no apparent outliers or other unusual characteristics. j) Give the value of the sample mean heart rate. Give the value of the sample median heart rate. Sample mean heart rate is beats per minute. Sample median heart rate is 72 beats per minute. 2

3 k) Give the value of the sample standard deviation for male heart rate. The sample standard deviation is 4.7 beats per minute. l) Construct side-by-side box plots (use a common scale) and use these to compare the distribution of females and males heart rates. Heart Rate F Gender M Males heart rate is slightly higher on average than females. Females also show more variation, or spread, than males do. It is hard to see the left skew shape in the box plot for females but the symmetric box plot for males confirms our earlier observation. 2. JMP Assignment: What is a normal body temperature? Researches took the body temperature (degrees Fahrenheit) of 130 adults, 65 males and 65 females. The data are in a file on the course web page. Follow the instructions in the JMP Guide to download the data from the web and open the data in JMP. a) Obtain a histogram, box plot, stem-and-leaf display and descriptive statistics for the body temperature. Print the JMP output and turn it in with your assignment. Use the output to answer the following questions. Describe the distribution of body temperature. Make sure to mention the shape, center, spread and any outliers. The shape of the distribution of body temperature is fairly symmetric. The center is around 98.3 degrees Fahrenheit. The data is spread from 96.3 to degrees Fahrenheit. The box plot indicates three potential outliers; two on the low end (96.3 and 96.4 degrees F) and one on the high end (100.8 degrees F) 3

4 What percentage of body temperatures are less than 98.6 degrees Fahrenheit? 81 out of 130 or 62.3% of the body temperatures are less than 98.6 degrees Fahrenheit. What is the sample median body temperature? What is the sample mean body temperature? The sample median body temperature is 98.3 degrees Fahrenheit. The sample mean body temperature is degrees Fahrenheit. Comment on the relationship between the sample median and sample mean and how this relationship is consistent with your description of the shape of the distribution. The sample median and the sample mean are almost equal. This is consistent with the description of the shape of the distribution as symmetric. b) Obtain histograms and descriptive statistics for the body temperature by gender. Make sure histograms have common scales. Also obtain side-by-side box plots for males and females. Print the JMP output and turn it in with your assignment. Use the output to answer the following questions. Compare males and females in terms of body temperature. Females tend to have slightly higher body temperatures than males. The sample mean and sample median for females are o F and o F, respectively while the sample mean and median for males is o F. Both distributions are fairly symmetric. There are a few potential outliers for the females, the temperature of o F is unusually high while temperatures of 96.4, 96.7 and 96.8 o F are unusually low. Looking at all of the values, the females have a larger standard deviation, o F, than the males, o F. Ignoring these potential outliers, the two distributions have about the same spread. 4

5 Distribution of Body Temperature for a sample of 130 adults Body Temperature (F) Stem Leaf represents 96.3 Quantiles Moments 100.0% maximum Mean % quartile Std Dev % median N % quartile % minimum

6 Gender=F (Female) Gender=M (Male) Quantiles 100.0% maximum % maximum % quartile % quartile % median % median % quartile % quartile % minimum % minimum Moments Mean Mean Std Dev Std Dev N 65 N Temp F M Gender Means and Std Deviations Level Number Mean Std Dev F M

AP * Statistics Review. Descriptive Statistics

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