Lesson 11

Comparing and Contrasting Data Distributions

  • Let’s investigate variability using data displays and summary statistics.

Problem 1

In science class, Clare and Lin estimate the mass of eight different objects that actually weigh 2,000 grams each.

Some summary statistics:

Clare

  • mean: 2,000 grams
  • MAD: 275 grams
  • median: 2,000 grams
  • IQR: 500 grams

Lin

  • mean: 2,000 grams
  • MAD: 225 grams
  • median: 1,950 grams
  • IQR: 350 grams

Which student was better at estimating the mass of the objects? Explain your reasoning.

Problem 2

A reporter counts the number of times a politician talks about jobs in their campaign speeches. What is the MAD of the data represented in the dot plot?

Dot plot from 2 to 9 by 1’s. Number of mentions of the word “jobs.” Beginning at 2, number of dots above each increment is 0, 1, 1, 3, 3, 1, 1, 0.
A:

1.1 mentions

B:

2 mentions

C:

2.5 mentions

D:

5.5 mentions

Problem 3

Four amateur miniature golfers attempt to finish 100 holes under par several times. Each round of 100, the number of holes they successfully complete under par is recorded. Due to the presence of extreme values, box plots were determined to be the best representation for the data. List the four box plots in order of variability from least to greatest.

player a

Box plot from 40 to 70 by 3’s. Number of holes completed under par. Whisker from 42 to 55. Box from 55 to 61 with vertical line at 57. Whisker from 61 to 66.

player b

Box plot from 40 to 70 by 3’s. Number of holes completed under par. Whisker from 48 to 55. Box from 55 to 64 with vertical line at 57. Whisker from 64 to 66.

player c

Box plot from 40 to 70 by 3’s. Number of holes completed under par. Whisker from 43 to 55. Box from 55 to 58 with vertical line at 56. Whisker from 58 to 67.

player d

Box plot from 40 to 70 by 3’s. Number of holes completed under par. Whisker from 41 to 43. Box from 43 to 55 with vertical line at 50. Whisker from 55 to 58.

Problem 4

Select all the distribution shapes for which the median could be much less than the mean.

A:

symmetric

B:

bell-shaped 

C:

skewed left

D:

skewed right 

E:

bimodal

(From Unit 1, Lesson 10.)

Problem 5

  1. What is the five-number summary for the data 0, 2, 2, 4, 5, 5, 5, 5, 7, 11?
  2. When the minimum, 0, is removed from the data set, what is the five-number summary?
(From Unit 1, Lesson 9.)

Problem 6

What effect does eliminating the highest value, 180, from the data set have on the mean and median?

25, 50, 50, 60, 70, 85, 85, 90, 90, 180

(From Unit 1, Lesson 9.)

Problem 7

The histogram represents the distribution of the number of seconds it took for each of 50 students to find the answer to a trivia question using the internet. Which interval contains the median?

Histogram from 0 to 30 by 5’s. Time in seconds. Beginning at 0 up to but not including 5, height of bar at each interval is 22, 5, 8, 9, 5, 1.
A:

0 to 5 seconds

B:

5 to 10 seconds

C:

10 to 15 seconds

D:

15 to 20 seconds

(From Unit 1, Lesson 3.)