Question

Scores turned in by an amateur golfer at a golf course during 2017 and 2018 are as follows.

2017 Season 73 77 78 76 74 72 74 76
2018 Season 70 69 74 76 84 79 70 78

Calculate the mean (to the nearest whole number) and the standard deviation (to 2 decimals) of the golfer's scores, for both years.

Answer 1

For 2017 Season:

Mean = 75

Standard deviation = 2.07

For 2018 Season:

Mean = 75

Standard deviation = 5.26

Explanation:

The following formulas will be used in these calculations:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

Standard deviation = Variance^0.5

Where;

n = number of values = 8

x = each value

For 2017 Season

Mean = (73 + 77 + 78 + 76 + 74 + 72 + 74 + 76) / 8 = 600 / 8 = 75

Variance = ((73-75)^2 + (77-75)^2 + (78-75)^2 + (76-75)^2 + (74-75)^2 + (72-75)^2 + (74-75)^2 + (76-75)^2) / (8-1) = 30 / 7 = 4.29

Standard deviation = Variance^0.50 = 4.29^0.5 = 2.07

For 2018 Season

Mean = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78) / 8 = 75

Variance = ((70-75)^2 + (69-75)^2 + (74-75)^2 + (76-75)^2 + (84-75)^2 + (79-75)^2 + (70-75)^2 + (78-75)^2) / (8-1) = 194 / 7 = 27.71

Standard deviation = Variance^0.50 = 27.71^0.5 = 5.26