The National Football League (NFL) polls fans to develop a rating for each football game (NFL website, October 24, 2012). Each game is rated on a scale from 0 (forgettable) to 100 (memorable). The fan ratings for a random sample of 12 games follow. 57 61 86 74 72 73 20 57 80 79 83 74 a. Develop a point estimate of mean fan rating for the population of NFL games. b. Develop a point estimate of the standard deviation for the population of NFL games.

The point estimate is a single value. The point estimate for the mean is the mean of the sample. In this case, the mean is the sum of the values divided by the total number of values. The point estimate is the standard deviation of the sample. The standard deviation is the square root of the variance.

See the attached photo for the calculations of these values.

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shivishivangi1679 shivishivangi1679 · Answer 2 · 2022-06-13T08:18:30+02:00

The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.

What is a point Estimate?

A) In order to find the point estimate of the mean, we will add up the data and divide it by the number of values.

Here,

∑x = 57 + 61 + 86 + 74 + 72 + 73 + 20 + 57 + 80 + 79 + 83 + 74

= 816

n = 12 numbers

Thus;

Mean = ∑x/n

= 816/12

Mean = 68

B) In order to find the estimate of the standard deviation, we have the formula;

s = √[(n*(∑x²) - (∑x)²)/n(n - 1)]

∑x² = 57² + 61² + 86² + ... + 74²

= 59,010

s = √[ (12*(59,010) - (816)²)/(12)(11)]

s = 17.6

Hence, The point estimates for the mean and standard deviation of the given data set is respectively; 68 and 17.6.

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