Question

On Monday, a class of students took a big test, and the highest score was 92. The next day, a student who had been absent made up the test, scoring 100. Indicate whether adding that student's score to the rest of the data made each of these summary statistics increase, decrease or stay the same:

Mean

Median

Range

IQR

Standard deviation

Answer 1

Adding 100 to the summary statistics:

• Mean - Increases

Since the previous high score was 92, adding another higher score(100) would increase the mean

• Median - Increases

Median is the middle value. It will shift to the right towards a higher value as well on adding 100

• Range - Increase

The range would definitely increase as the maximum value is now more (from 92 to 100)

• IQR - Q3 - Q1 - Can increase, decrease or remain the same.

Both Q3 and Q1 will increase to the right. So IQR can move in all 3 directions.

• Standard deviation - Increases

Now we have an additional outlier value which would increase the standard deviation.

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