Question

. Golf A local high school golf team has eight members on their team. The scores (measured in strokes) for the first match of the season are listed below for each of the eight members. Answer this question without the use of JMP.
77 91 75 69 80 74 88 88
(a) Calculate the mean score for the high school golf team during their first match. Keep all decimal places.
(b) Calculate the median score for the high school golf team during their first match. Keep all decimal places.
(c) Fill in the blank Suppose the player with the reported best score (in golf a lower score is better) in the lineup above actually scored a 76, i.e. replacing the lowest score above by 76. The mean score of the eight golf scores would_____. The median score of the eight golf scores would ____. We conclude that the ____ is robust to extreme observations based on the first two answers.
i. stay the same, increase, median
ii. increase, decrease, median
iii. increase, stay the same, mean
iv. increase, stay the same, median
v. increase, increase, median
(d) The variance of the eight scores (after replacing the lowest score by 76 as described above) is 46.4107. Calculate the standard deviation. Round final answer to the nearest TWO decimal places.

Answer 1

Answer)

A)

Mean = (sum of the observations)/(number of observations)

= (77 + 91 ....)/8

= 80.25

B)

To find the median, first we need to arrange the data in ascending order

= 69, 74, 75, 77, 80, 88, 88, 91

Median is (77+80)/2

= 78.5

C)

Lowest score is 69

So we will replace 69 with 76

Mean = 81.125

Mean is increased

Now for median new data would be

74, 75, 76, 77, 80, 88, 88, 91

Still median is same here

So median stays the same

D)

Standard deviation is square root of variance

Given variance is 46.4107

S.d = √{46.4107}

= 6.81253990813

= 6.81