Lesson 7
Using Histograms to Answer Statistical Questions
Problem 1
These two histograms show the number of text messages sent in one week by two groups of 100 students. The first histogram summarizes data from sixth-grade students. The second histogram summarizes data from seventh-grade students.
![Two histograms, text messages sent per week by sixth grade students and seventh grade students,](https://cms-im.s3.amazonaws.com/6YR5K2YepTBK9quSTqo5b1dL?response-content-disposition=inline%3B%20filename%3D%226-6.8.B.PP.Image.17smush.png%22%3B%20filename%2A%3DUTF-8%27%276-6.8.B.PP.Image.17smush.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171725Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6b178f75e30f0e263aa9cffc0d5dbf67190f83ab3a6e964eb464fdfd6a27ee74)
- Do the two data sets have approximately the same center? If so, explain where the center is located. If not, which one has the greater center?
- Which data set has greater spread? Explain your reasoning.
- Overall, which group of students—sixth- or seventh-grade—sent more text messages?
Solution
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Problem 2
Forty sixth-grade students ran 1 mile. Here is a histogram that summarizes their times, in minutes. The center of the distribution is approximately 10 minutes.
On the blank axes, draw a second histogram that has:
- a distribution of times for a different group of 40 sixth-grade students.
- a center at 10 minutes.
- less variability than the distribution shown in the first histogram.
![A histogram from 2 to 16 by twos. Beginning at 2 up to but not including 4, height of bar at each interval is 0, 1, 5, 13, 12, 7, 2.](https://cms-im.s3.amazonaws.com/jpEeeE2ybZbXrn9iPtUGMKE5?response-content-disposition=inline%3B%20filename%3D%226-6.8.B.PP.Image.21b.png%22%3B%20filename%2A%3DUTF-8%27%276-6.8.B.PP.Image.21b.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171725Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0c3323da57501684c3250d7d7223c98b13172064d96ded52aa102ddef586721d)
![Blank axes for drawing a histogram. Horizontal axes labeled 2 though 16 by twos. Vertical axes, tick marks 0 through 14 by ones, only 0 and even numbers labeled.](https://cms-im.s3.amazonaws.com/8oGFE1TPYMNqATRHpY3HP3qq?response-content-disposition=inline%3B%20filename%3D%226-6.8.B.PP.Image.Revision.21c.png%22%3B%20filename%2A%3DUTF-8%27%276-6.8.B.PP.Image.Revision.21c.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T171725Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a736c3e1af2762aee528ad43e40648fbe9783e660d967f11bb1bf56de4e47d91)
Solution
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Problem 3
Jada has \(d\) dimes. She has more than 30 cents but less than a dollar.
- Write two inequalities that represent how many dimes Jada has.
- Can \(d\) be 10?
- How many possible solutions make both inequalities true? If possible, describe or list the solutions.
Solution
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(From Unit 7, Lesson 9.)Problem 4
Order these numbers from greatest to least: \(\text-4\), \(\frac14\), 0, 4, \(\text{-}3\frac{1}{2}\), \(\frac74\), \(\text{-}\frac{5}{4}\)
Solution
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(From Unit 7, Lesson 4.)