Lesson 10

The Effect of Extremes

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Problem 1

Select all the distribution shapes for which it is most often appropriate to use the mean.

A:

bell-shaped

B:

bimodal

C:

skewed

D:

symmetric

E:

uniform

Solution

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Problem 2

For which distribution shape is it usually appropriate to use the median when summarizing the data?

A:

bell-shaped

B:

skewed

C:

symmetric

D:

uniform

Solution

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Problem 3

The number of writing instruments in some teachers' desks is displayed in the dot plot. Which is greater, the mean or the median? Explain your reasoning using the shape of the distribution.

Dot plot from 4 to 13 by 1's. Number of writing instruments. Beginning at 4, number of dots above each increment is 0, 1, 1, 1, 1, 3, 4, 2, 1, 0.  

Solution

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Problem 4

A student has these scores on their assignments. The teacher is considering dropping a lowest score. What effect does eliminating the lowest value, 0, from the data set have on the mean and median?

0, 40, 60, 70, 75, 80, 85, 95, 95, 100

Solution

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(From Unit 1, Lesson 9.)

Problem 5

  1. What is the five-number summary for the data 2, 2, 4, 4, 5, 5, 6, 7, 9, 15?
  2. When the maximum, 15, is removed from the data set, what is the five-number summary?

Solution

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(From Unit 1, Lesson 9.)

Problem 6

The box plot summarizes the test scores for 100 students:

Boxplot from 55 to 100 by 5’s. test scores. Whisker from 55 to 85. Box from 85 to 95 with a vertical line at 92. Whisker from 95 to 100.

Which term best describes the shape of the distribution?

A:

bell-shaped

B:

uniform

C:

skewed

D:

symmetric

Solution

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(From Unit 1, Lesson 4.)

Problem 7

The histogram represents the distribution of lengths, in inches, of 25 catfish caught in a lake.

Histogram from 0 to 18 by 3’s represents "catfish length, inches." Beginning at 0 up to but not including 3, height of bar at each interval is 0, 4, 9, 5, 6, 1.
  1. If possible, find the mean. If not possible, explain why not.
  2. If possible, find the median. If not possible, explain why not.
  3. Were any of the fish caught 12 inches long?
  4. Were any of the fish caught 19 inches long?

Solution

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(From Unit 1, Lesson 2.)