The longest running U.S.-produced fictional content television show by number of

Question

The longest running U.S.-produced fictional content television show by number of episodes is Gunsmoke, Other long-running shows of this type include Lassie, Ozzie and Harriett, and Bonanza. Law and Order is currently number 10 with approximately 350 shows. The number of episodes for some of the top 115 shows are given in the following table. a. Find the median, the first and third quartile, and the interquartile range. b. Find the 30th and the 95th percentiles. c. Suppose the Simpsons currently have 438 episodes (as of November 2008). Using the data in the table, in what percentile does this episode count lie?

Explanation / Answer

a.) Median = (n+1)/2 largest data point = the average of the 13th and 14th ordered points = (236 + 251)/2 = 243.5

First quartile = .25(N+1)th ordered point = 6.75th ordered point = 199 + .75(200-199) = 199.75

Third quartile = .75(N+1)th ordered point = 20.25th ordered point = 361 +.25(369-361) = 363

Interquartile range = 363 - 199.75 = 163.25

b) 30th Percentile:

Index = 0.30 * (26+1) = 8.1

Round it up to the nearest whole number = 8

Count to 8 from smallest to largest number = 201 (This is the 30th percentile)

90th percentile:

Index = 0.90 * (26+1) = 24.3

Round it up to the nearest whole number = 24

Count to 24 from smallest to largest number = 435 (This is the 90th percentile)

c) Percentile = L + ( 0.5 x S ) / N

Where, L = Number of below rank, S = Number of same rank, N = Total numbers.

L = 24

S = 0

N = 26

Percentile = 92.31

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