Lesson 5

Calculating Measures of Center and Variability

  • Let’s calculate measures of center and measures of variability and know which are most appropriate for the data.

Problem 1

The data set represents the number of errors on a typing test.

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  1. What is the median? Interpret this value in the situation.
  2. What is the IQR?

Problem 2

The data set represents the heights, in centimeters, of ten model bridges made for an engineering competition.

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  1. What is the mean?
  2. What is the MAD?

Problem 3

Describe the shape of the distribution shown in the dot plot. The dot plot displays the golf scores from a golf tournament.

Dot plot from 132 to 140 by 1’s. golf score (strokes). Beginning at 132, number of dots above each increment is 0, 2, 3, 6, 3, 2, 2, 6, 1, 1.

 

(From Unit 1, Lesson 4.)

Problem 4

The dot plot shows the weight, in grams, of several different rocks. Select all the terms that describe the shape of the distribution.

Dot plot from 0.24 to 0.34 by .01’s. weight (grams). Beginning at 0.24, number of dots above each increment is 0, 2, 4, 6, 4, 2, 4, 6, 4, 2, 0.
A:

bell-shaped

B:

bimodal

C:

skewed

D:

symmetric

E:

uniform

(From Unit 1, Lesson 4.)

Problem 5

The dot plot represents the distribution of wages earned during a one-week period by 12 college students.

Dot plot from 112 to 124 by 1’s. Weekly wages in dollars. Beginning at 112, number of dots above each increment is 1, 1, 0, 0, 3, 0, 2, 2, 0, 0, 0, 0, 3.  
  1. What is the mean? Interpret this value based on the situation.
  2. What is the median? Interpret this value based on the situation.
  3. Would a box plot of the same data have allowed you to find both the mean and the median?
(From Unit 1, Lesson 3.)

Problem 6

The box plot displays the temperature of saunas in degrees Fahrenheit. What is the median?

Box plot from 110 to 126 by 2’s labeled "degrees, Fahrenheit". Whisker from 111 to 115. Box from 115 to 124 with vertical line at 118. Whisker from 124 to 126. 
(From Unit 1, Lesson 2.)