Practice Problems: Measures of Variability - Answer

A group committed to quality television has been concerned about a new talk show. For two weeks, they decide to count the number of words that must be "bleeped" as too obscene for television and the number of physical altercations. They hope that after recording this data that they will be able to argue that the show is inappropriate for television particularly during the day. The data for number of words censored is provided below.

X X2
349121801
342116964
321103041
28983521
26771289
25464516
16627556
15724649
13217424
33 1089
2310631850


Standard Deviation

S = 10 (631850) - 23102
10 (10 - 1)

S = 104.47754

Variance

The variance is 10915.556. The standard deviation is 104.47754. The variance is the square of the standard deviation. 104.47754 squared is equal to 10915.556.

S2 = 10915.556

Range

The range is 316. The high score is 349; the low score is 33. 349 - 33 = 316.

Range = 316

What does this information tell you about variability of number of words censored during the talk show?

The variability is quite high. The standard deviation is approximately 104 words. Considering that most shows have no words needing to be regularly censored, a mean of 231 with a standard deviation of 104 is outside of the norm.

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