Lesson 7: Practice Problems

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.

histogram of text messages sent by sixth-grade students

histogram of text messages sent by seventh-grade students

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?

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.

A histogram. The horizontal axis has the numbers 2 through 16 indicated in increments of 2. The vertical axis has the numbers 0 through 14 indicated, in increments of 2. There are tick marks midway between. The data represented by the bars are as follows: from 4 up to 6 minutes, 1; from 6 up to 8 minutes, 5; from 8 up to 10 minutes, 13; from 10 up to 12 minutes, 12; from 12 up to 14 minutes, 7; from 14 up to 16 minutes, 2.

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 blank axis with the horizontal scale from 2 to 16 and the vertical scale from 0 to 14.

Problem 3 From Unit 7 Lesson 9

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.

Problem 4 From Unit 7 Lesson 4

Order these numbers from greatest to least:

$- 4$
$\frac{1}{4}$
$0$
$4$
$- 3 \frac{1}{2}$
$\frac{7}{4}$
$- \frac{5}{4}$