Mode, median, range

Question

John tried the golf club that his Daughter Mary gave him for his birthday. He hit golf balls the following distances (measured in yards): 101, 94, 87, 101, 93, 108, 84, 93, 107, 95, 103, 113, 86, 107, 105, 96, 101, 117, 108, 105.

(a) Find range, median, and mode

(b) determine the percentage of the distances that were less than 100 yards.

Answer 1

Distances from minimum to maximum: 84, 86, 87, 93, 93, 94, 95, 96, 101,101, 101, 103, 105, 105, 107, 107, 108, 108, 113, 117 - for a total of 20 points.

a.

The range of these 20 points is from 84 to 117 or:

Range: 117 - 84 + 1 = 34

The median is the value at midspan. With an even number of points the midspan is between two numbers - in this case, numbers 10 & 11 (101 & 101) - which averages to 101.

Median = (101 + 101)/2 = 101

The mode corresponds to the most common value (value repeated the most.)

Mode = 101

b:

Total number of distance values less than 100 is 8. Since the total number of values is 20:

% (<100) = 8/20=.040 = 40%