Question

The National Football League (NFL) polls fans to develop a rating for each football game. 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	62	87	73	72	72
20	56	79	78	83	73

b. Develop a point estimate of the standard deviation for the population of NFL games (to 4 decimals).

Answer 1

ANSWER:

Point estimate is the single value and is given as an estimate of the population and in this case we will find the standard deviation which means that from the mean rating how much the individual rating differs.

formula for point estimate of standard deviation = ( ( ( n * x^2 ) - ( x) ^ 2 ) / n (n-1) ) ^ 1 / 2

where n = 12

x = sum of all the raings

(x) ^ 2 = (57 + 62 + 87 + 73 + 72 + 72 + 20 + 56 + 79 + 78 + 83 + 73 ) = (812)^ 2 = 659,344

x^2 = (57) ^ 2 + (62) ^2 + (87) ^2 + (73) ^2 + (72) ^2 + (72) ^2 + (20) ^ 2 + (56) ^ 2 + (79) ^ 2 + (78) ^ 2 + (83) ^2 + ( 73) ^ 2

x^2 = 3249 + 3844 + 7569 + 5329 + 5184 + 5184 + 400 + 3136 + 6241 + 6084 + 6889 + 5329 = 58,438

point estimate of standard deviation = ( ( 12 * 58,438) - ( 659,344) ) / (12 / ( 12 - 1) ) ^ 1 / 2

point estimate of standard deviation = ( ( 701,256 - 659,344) / ( 12 * 11) ^ 1 / 2

point estimate of standard deviation = (41,912 / 132) ^ 1 / 2 = (317.51 ) ^ 1 / 2 = 17.81