Question

Golf Tournament In a golf tournament, the top 6 men's scores are 65, 68, 70, 72, 73, 75. The top women's scores are 69, 71, 73, 74, 77, 80. Compare the spread of the data for the two sets of scores using (a) the range and (b) the mean absolute deviation.

Answer 1

Answer:
Range: Men: 10, Women: 11
MAD: Men: 2.833333 (17/6), Women: 3

Explanation:

The range of the men's scores is 75-65 (highest-lowest), which is 10.

The range of the woman's scores is 80-69, which is 11.

The MAD is the mean of the absolute difference between the terms and the mean, which is very painful to do, but in the sake of the problem, I will be doing.

Men's MAD:
The mean is
`(65+68+70+72+73+75)/(6)`, which is 70.5.

Sigh.

Now, we find the difference of each term to the mean.

`70.5-65= 5.5`

`70.5-68=2.5`

`70.5 - 70 = 0.5`

`72-70.5=1.5`

`73-70.5=2.5`

`75-70.5=4.5`

wow. Now, we find the mean of these numbers.

`(5.5 + 2.5 + 0.5 + 1.5 + 2.5 + 4.5)/(6)`= 17/6=2.8333333333 This is the MAD.

For the Women's, I'll speed over it.

The mean is 74.

The MAD is 3.