A data entry is an outlier if it is more than one-and-a-half times the inter-quartile range above Q3 or below Q1.

To find out if the score of 32 is really an outlier, first compute the IQR of the data set for the original scores in Mr. Sneed’s class given in Practice Problem #1a.

IQR = Q_{3 }- Q_{1 }= 82 – 66 = 16 1.5 x IQR = 1.5 x 16 = 24

# Is 32 far enough below Q_{1 }to be classified an outlier? Let’s see:

# Q_{1 }- 24 = 66 – 24 = 42

The score of 32 is below 42, so 32 is an outlier.

# Is 98 an outlier in the other direction?

1.5 x IQR = 1.5 x 16 = 24 Q_{3 }+ 24 = 82 + 24 = 106

The score of 98 is less than 106, so 98 is not an outlier.

# Practice problem:

7. In “Ages of Oscar-Winning Best Actors and Actresses” (Mathematics Teacher magazine) by Richard Brown and Gretchen Davis, stem-and-leaf plots are used to compare the ages of actors and actresses at the time they won Oscars. Below are the ages for 34 recent Oscar winners in each gender category:

# Actors:

32 37 36 51 53 33 61 35 45 55 39 76 37 42 40 32 32 60 38 56 48 48 40 43 62 43 42 44 41 56 39 46 31 47

Actresses: 50 44 35 80 26 28 41 21 61 38 49 33 74 30 33 41 31 35 41 42 37 26 34 34 35 26 61 60 34 24 30 37 31 27

a)

Construct a back-to-back stem-and-leaf plot for the above data, using the tens digits for the stems. Discuss shape, center and spread for each data set, comparing the two sets and discussing any differences you see.

b)

Construct two box-and-whisker plots on the same graph to compare ages of actors and actresses at the time they won Oscars. What do you observe? Write a short paragraph discussing the bottom 25% of ages, the middle 50% of ages and the top 25% of ages, and discuss difference you observe in the data sets. What conclusions can you draw?

c)

Are there any outliers in the data sets? Verify your answer.

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