Lesson 3

A Gallery of Data

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Problem 1

The box plot represents the distribution of speeds, in miles per hour, of 100 cars as they passed through a busy intersection.

Box plot from 4 to 48 by 4’s. Speed of car in miles per hour. Whisker from 8 to 12. Box from 12 to 24 with vertical line at 20. Whisker from 24 to 44.  
  1. What is the smallest value in the data set? Interpret this value in the situation.
  2. What is the largest value in the data set? Interpret this value in the situation.
  3. What is the median? Interpret this value in the situation.
  4. What is the first quartile (Q1)? Interpret this value in the situation.
  5. What is the third quartile (Q3)? Interpret this value in the situation.

Solution

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Problem 2

The data set represents the number of eggs produced by a small group of chickens each day for ten days: 7, 7, 7, 7, 7, 8, 8, 8, 8, 9. Select all the values that could represent the typical number of eggs produced in a day.

A:

7.5 eggs

B:

7.6 eggs

C:

7.7 eggs

D:

8 eggs

E:

9 eggs

Solution

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Problem 3

The dot plot displays the lengths of pencils (in inches) used by students in a class. What is the mean?

Dot plot from 5 to 7 by 0.5’s. Length(inches). Beginning at 5, number of dots above each increment is 1, 2, 4, 2, 1.

Solution

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(From Unit 1, Lesson 2.)

Problem 4

The histogram represents ages of 40 people at a store that sells children's clothes. Which interval contains the median?

Histogram from 0 to 35 by 5’s. age (years). Beginning at 0 up to but not including 5, height of bar at each interval is 10, 8, 6, 3, 5, 3, 4.
A:

The interval from 0 to 5 years.

B:

The interval from 5 to 10 years.

C:

The interval from 10 to 15 years.

D:

The interval from 15 to 20 years.

Solution

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(From Unit 1, Lesson 2.)

Problem 5

The data set represents the responses, in degrees Fahrenheit, collected to answer the question “How hot is the sidewalk during the school day?”.

92, 95, 95, 95, 98, 100, 100, 100, 103, 105, 105, 111, 112, 115, 115, 116, 117, 117, 118, 119, 119, 119, 119, 119, 119

  1. Create a dot plot to represent the distribution of the data.
  2. Create a histogram to represent the distribution of the data.
  3. Which display gives you a better overall understanding of the data? Explain your reasoning.

Solution

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(From Unit 1, Lesson 2.)

Problem 6

Is “What is the area of the floor in this classroom?” a statistical question? Explain your reasoning.

Solution

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(From Unit 1, Lesson 1.)