Chapter 15.1, Problem 16WE

To determine

Identify the affect on mode, median and mean.

Answer to Problem 16WE

Each should be reduced by $40\%$ .

Explanation of Solution

Given information:

If each score in a set of scores were reduced by $40\%$ ,

Calculation:

The mode is the number that occurs most frequently. So each score is reduced by $40\%$ , the frequently occurring score would also reduced by $40\%$ and hence the mode of the new set of scores would be $40\%$ less that the mode of the original data set.

The mean is the arithmetic average of the numbers. So it is computed by dividing the sum of the observations by the number of observations in the sidtribution. If each score is reduced by $40\%$ then their sum would also be decreased by $40\%$ , hence the leading to a reduction of the average by $40\%$ . Hence, the mean of the new set of scores would be $40\%$ less than the mean of the original data set.

The median is the observation that divides the distribution into two halves. If the data set contains odd number of observations, the middle observation would be median. If we reduced each score by $40\%$ , the middle observation will also be reduced by $40\%$ and hence the median of the new data set will be $40\%$ less than the median of the original data set.

If the data set contains even number of observations, the median is the mean of the two middle observations. As we see from the previous step, if we reduce each score by $40\%$ , then the mean of the new set of scores would be $40\%$ less than the mean of the original data set.

Hence, if we reduce each score by $40\%$ , the mean of the middle two numbers would be reduced by $40\%$ .

Hence, even in the case of even number of observations, the median of the new data set will be $40\%$ less than the median of the original data set.

Hence, each should be reduced by $40\%$ .