Download For Exercises 5 and 6, complete each step. a. Use a graphing

11-2 Distributions of Data
For Exercises 5 and 6, complete each step.
a. Use a graphing calculator to create a histogram and a box-and-whisker plot. Then describe the shape
of the distribution.
b. Describe the center and spread of the data using either the mean and standard deviation or the fivenumber summary. Justify your choice.
6. MOVIES The students in one of Mr. Peterson’s classes recorded the number of movies they saw over the past
month.
SOLUTION: a.
Histogram:
First, press STAT ENTER and enter each data value. Then, press 2ND [STAT PLOT] ENTER ENTER and
choose „ . Finally, adjust the window to the dimensions shown.
Box-and-whisker Plot: Press 2ND [STAT PLOT] ENTER ENTER and choose fl. Adjust the window to the
dimensions shown.
The date are equally distributed on each side of the mean, so the distribution is symmetric.
b. The distribution is symmetric, so use the mean and standard deviation. Press STAT ► ENTER ENTER and
scroll down to view the mean and standard deviation.
eSolutions Manual - Powered by Cognero
The mean number of movies watched was about 10.7 with standard deviation of about 3 movies.
Page 1
For Exercises 5 and 6, complete each step.
a. Use a graphing calculator to create a histogram and a box-and-whisker plot. Then describe the shape
the distribution.
11-2of
Distributions
of Data
b. Describe the center and spread of the data using either the mean and standard deviation or the fivenumber summary. Justify your choice.
6. MOVIES The students in one of Mr. Peterson’s classes recorded the number of movies they saw over the past
month.
SOLUTION: a.
Histogram:
First, press STAT ENTER and enter each data value. Then, press 2ND [STAT PLOT] ENTER ENTER and
choose „ . Finally, adjust the window to the dimensions shown.
Box-and-whisker Plot: Press 2ND [STAT PLOT] ENTER ENTER and choose fl. Adjust the window to the
dimensions shown.
The date are equally distributed on each side of the mean, so the distribution is symmetric.
b. The distribution is symmetric, so use the mean and standard deviation. Press STAT ► ENTER ENTER and
scroll down to view the mean and standard deviation.
The mean number of movies watched was about 10.7 with standard deviation of about 3 movies.
CCSS TOOLS Complete each step.
a. Use a graphing calculator to create a histogram for each data set. Then describe the shape of each
distribution.
b. Compare the distributions using either the means and standard deviations or the five-number
eSolutions Manual - Powered by Cognero
Page 2
11-2The
Distributions
of Data
mean number
of movies watched was about 10.7 with standard deviation of about 3 movies.
CCSS TOOLS Complete each step.
a. Use a graphing calculator to create a histogram for each data set. Then describe the shape of each
distribution.
b. Compare the distributions using either the means and standard deviations or the five-number
summaries. Justify your choice.
7. SAT A group of students took the SAT their sophomore year and again their junior year. Their scores are shown.
SOLUTION: a.
Sophomore Year:
First, press STAT ENTER and enter each data value. Then, press 2ND [STAT PLOT] ENTER ENTER and
choose „ . Finally, adjust the window to the dimensions shown.
The data are evenly distributed, so the distribution is symmetric.
Junior Year:
First, press STAT ENTER and enter each data value in L2. Then, press 2ND [STAT PLOT] ENTER ENTER
and choose „ . Finally, adjust the window to the dimensions shown.
The data are evenly distributed, so the distribution is symmetric.
eSolutions Manual - Powered by Cognero
b. The distributions are symmetric, so use the means and standard deviations.
For the first distribution, press STAT ► ENTER ENTER and scroll down to view the mean and standard
Page 3
11-2 Distributions of Data
The data are evenly distributed, so the distribution is symmetric.
b. The distributions are symmetric, so use the means and standard deviations.
For the first distribution, press STAT ► ENTER ENTER and scroll down to view the mean and standard
deviation. For the second distribution, press STAT ► ENTER ENTER L2 and scroll down to view the mean and
standard deviation.
Sophomore Year:
Junior Year:
The mean score for sophomore year is about 1552.9 with standard deviation of about 147.2. The mean score for
junior year is about 1753.8 with standard deviation of about 159.1. We can conclude that the scores and the variation
of the scores from the mean both increased from sophomore year to junior year.
11. BASKETBALL Refer to the beginning of the lesson. The points that Craig scored in the remaining games are
shown.
a. Use a graphing calculator to create a box-and-whisker plot. Describe the center and spread of the data. b. Craig scored 0, 2, 1, and 0 points in the first four games. Use a graphing calculator to create a box-and-whisker
plot that includes the new data. Then find the mean and median of the new data set.
c. What effect does adding the scores from the first four games have on the shape of the distribution and on how
you should describe the center and spread?
SOLUTION: a. Enter the data as L1. Press 2ND [STAT PLOT] ENTER ENTER and choose fl. Adjust the window to the
dimensions shown.
eSolutions Manual - Powered by Cognero
Page 4
you should describe the center and spread?
SOLUTION: Enter the dataofasData
L1. Press 2ND [STAT PLOT] ENTER ENTER and choose fl. Adjust the window to the
11-2a.Distributions
dimensions shown.
The distribution is symmetric, so use the mean and standard deviation.
The mean of the data is 18 with a sample standard deviation of about 5.2 points.
b. Add the new data to L1. Press 2ND [STAT PLOT] ENTER ENTER and choose fl. Adjust the window to the
dimensions shown.
Find the new mean and median:
eSolutions Manual - Powered by Cognero
The new mean is 14.55 and the new median is 17.
Page 5
c. Adding the scores from the first four games causes the shape of the distribution to go from being symmetric to
11-2 Distributions of Data
The new mean is 14.55 and the new median is 17.
c. Adding the scores from the first four games causes the shape of the distribution to go from being symmetric to
being negatively skewed. Therefore, the center and spread should be described using the five-number summary.
13. CHALLENGE Approximate the mean and median for each distribution of data.
a.
b.
c.
SOLUTION: a. Sample answer: Since the distribution is positively skewed, the median will be to the left of the mean closer to the
majority of the data. An estimate for the median is 10. The mean will be more affected by the tail, and will be to the
right of the majority of the data. An estimate for the mean is 14.
b. Sample answer: Since the distribution is negatively skewed, the median will be to the right of the mean closer to
the majority of the data. An estimate for the median is 24. The mean will be more affected by the tail, and will be to
the left of the majority of the data. An estimate for the mean is 20.
c. Sample answer: Since the distribution is symmetric, the mean and median will be approximately equal near the
middle of the data. An estimate for the mean and median is 17.
eSolutions Manual - Powered by Cognero
Page 6