Chapter 2, Section 4, Exercise 131 INVESTIGATING HOLLYWOOD MOVIES In the followi

ID: 3180842 • Letter: C

Question

Chapter 2, Section 4, Exercise 131 INVESTIGATING HOLLYWOOD MOVIES In the following exercise, we use data from HollywoodMovies2011. The dataset includes information on all 136 movies to come out of Hollywood in 2011. Audience Scores on Rotten Tomatoes Audience scores (on a scale from 1 to 100) on the Rotten Tomatoes website for all movies that came out of Hollywood in 2011 have a five number summary of (24,49,61,77,93). (These data are in the variable AudienceScore in the dataset HollywoodMovies2011.)

Variable Genre N Mean StDev Minimum Q1 Median Q3 Maximum

Audience Score Action 32 58.63 18.39 32.00 44.50 51.00 78.00 93.00

Animation 12 64.08 13.89 43.00 50.50 64.00 78.25 82.00

Comedy 27 59.11 15.68 31.00 48.00 58.00 71.00 93.00

Drama 21 72.10 14.55 46.00 59.00 72.00 84.50 91.00

Horror 17 48.65 15.88 25.00 34.00 52.00 60.50 78.00

Romance 10 64.80 12.90 50.00 52.25 65.50 78.00 84.00

Thriller 13 64.31 14.87 24.00 57.00 67.00 74.50 81.00

Are there any outliers in these scores? If there are no outliers, enter 0 in the answer box below. There is/are... outlier(s). How bad would an average audience score rating have to be on Rotten Tomatoes to qualify as a low outlier? Less than...

Explanation / Answer

Back-up Theory

Let Xbar and SD be the average and standard deviation of a set of n observations.

Any observation, say x, in the set of these n observations is considered an outlier if it lies outside the range (Xbar ± 3SD), i.e., x < Xbar – 3SD or x > Xbar + 3SD

Now, to work out solution,

Since the data is given genre-wise, the outliers also will have to be genre-wise.

All requisite computations are tabulated below:

Genre

Mean

(Xbar)

Xbar – 3SD

Xbar + 3SD

Minimum

Maximum

Action

58.63

18.39

3.46

113.8

Animation

64.08

13.89

22.41

105.75

78.25

Comedy

59.11

15.68

12.07

106.15

31.00

Drama

72.10

14.55

28.45

115.75

46.00

Horror

48.65

15.88

1.01

96.29

25.00

Romance

64.80

12.90

26.1

103.5

50.00

Thriller

64.31

14.87

19.7

108.92

24.00

Since individual observations are not available, we will check minimum and maximum observations against Xbar – 3SD and Xbar + 3SD

Part (a)

Since in none of the genres minimum is less than Xbar – 3SD or maximum is more than

Xbar + 3SD, there are no outliers ANSWER is 0.

Part (b)

Since there are no outliers, this part is not applicable. ANSWER

Part (c)

For each genre, Xbar – 3SD gives the minimum value acceptable for a value not to be an outlier. ANSWER