A company wanted to determine the child care costs of its employees. A sample of 25 employees were interviewed and their child care expenses for the previous year were determined. Later, the company discovered that the highest expense in the sample was mistakenly recorded as 5 times the actual amount. However, after correcting the error, the correct amount was still greater than or equal to any other expense in the sample. Which of the following sample statistics must have remained the same after the correction was made?
a) variance
b) mean
c) mode
d) range
e) median

1. The reason the answer is median is that, median is not affected by extreme or outlier value. This is simply because, the median is the middle number.

For instance, if I have the following observations:

2,1,3,4,5,6,7,8,10,3,4,5,6,7,8

And say, instead of 8, we mistakenly inputted 88.

2,1,3,4,5,6,7,8,10,3,4,5,6,7,88

If we solve for all the statistics in the option, only the median will remain the same.

################## TRY THIS IN R Programming####

s = c(2,1,3,4,5,6,7,8,10,3,4,5,6,7,8)

var(s) # Ans = 6.209524

mean(s) # Ans = 5.266667

range(s) # Ans = 9

median(s) # Ans = 5

s = c(2,1,3,4,5,6,7,8,10,3,4,5,6,7,88)

var(s) # Ans = 464.1143

mean(s) # Ans = 10.6

range(s) # Ans = 87

median(s) # Ans = 5

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2. Mode (with reservation, please see explanation)

2. On the second hand, mode is most occurrence values. Since we are told that, only the highest value was affected, it means that the mode too will remained the same.

This is just for information. The correct answer is MEDIAN!