Question

The ages of the racers in a bicycle motocross race are 14, 22, 20, 25, 26, 17, 21, 30, 27, 25, 14, and 29. The 30-year-old drops out of the race and is replaced with a 15-year-old. How are the mean, median, and mode of the ages affected?

Answer 1

The mean is decreased by 1.25.

The mode remains the same.

The median is decreased by 2 .

Explanation:

Re arranging the data 14, 22, 20, 25, 26, 17, 21, 30, 27, 25, 14, and 29.

Gives

14, 14,17,20, 21, 22, 25,25, 26, 27, 29,30,

Now the mean = 14, +14,+17, +20, +21,+ 22, +25,+25,+ 26, + 27, +29,+30/12

Mean= 270/12=22.5

The Mode ( the repeated value) = 14,25

Median ( the average of middle value) = 22+25/2= 23.5

When 30 is replaced is by 15

Now the mean = 14, +14, +15,+17, +20, +21,+ 22, +25,+25,+ 26, + 27, +29/12

The Mean becomes = 255/12=21.25

The Mode ( the repeated value) = 14,25

Median ( the average of the middle value) = 21+22/2= 21.5

The difference between the 2 means is = 22.5- 21.25= 1.25

The mode remains the same.

The median is decreased by 2 .

The mean is decreased by 1.25 which is more than 50 % of the value obtained between the ratio of the omitted and added value (30/15=) i.e. 2