Question

Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during and are as follows: Season: 75 79 80 78 76 74 76 78 Season: 72 71 76 78 86 81 72 80 a. Calculate the mean (to the nearest whole number) and the standard deviation (to decimals) of the golfer's scores, for both years. Mean 77 Standard deviation 2.07 Mean 77 Standard deviation 5.26 b. What is the primary difference in performance between and

Answer 1

Explained below.

Explanation:

The scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida are,

Season 1: {75, 79, 80, 78, 76, 74, 76, 78}

Season 2: {72, 71, 76, 78, 86, 81, 72, 80}

(a)

Compute the mean and standard deviation of the golfer's scores as follows:

Season 1:

`\bar x_(1)=(1)/(n_(1))\sum x_(1)\\\\=(1)/(8)* 616\\\\=77`

`s_(1)=\sqrt{(1)/(n-1)\sum(x_(1)-\bar x_(1))^(2)}\\\\=\sqrt{(1)/(8-1)* 30}\\\\=2.0702\\\\\approx 2.07`

Season 2:

`\bar x_(2)=(1)/(n_(2))\sum x_(2)\\\\=(1)/(8)* 616\\\\=77`

`s_(2)=\sqrt{(1)/(n_(2)-1)\sum(x_(2)-\bar x_(2))^(2)}\\\\=\sqrt{(1)/(8-1)* 194}\\\\=5.26444\\\\\approx 5.26`

(b)

The primary difference in performance between the two seasons is:

`\text{Diff} = \bar x_(2)-\bar x_(1)\\\\=5.26-2.07\\\\=3.19`