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Look at this set of $8$ numbers: $\newline$ $60, 27, 98, 30, 65, 27, 55, 51$ $\newline$ How would the median change if the number $31$ were added to the set? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease $\newline$ (C)no change

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Changes in mean, median, mode, and range

Full solution

Q. Look at this set of

8

numbers:

\newline

60, 27, 98, 30, 65, 27, 55, 51

\newline

How would the median change if the number

31

were added to the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Arrange Data in Ascending Order: Arrange the original data set in ascending order. $\newline$ Original data set: $27, 27, 30, 51, 55, 60, 65, 98$ .
Calculate Median of Original Data: Calculate the median of the original data set. $\newline$ Since there are $8$ numbers, the median is the average of the $4$ th and $5$ th numbers. $\newline$ $(51 + 55) / 2 = 53$
Add Number $31$ and Arrange: Add the number $31$ to the data set and arrange it in ascending order. $\newline$ New data set: $27, 27, 30, 31, 51, 55, 60, 65, 98$ .
Calculate Median of New Data: Calculate the median of the new data set. $\newline$ Since there are now $9$ numbers, the median is the $5$ th number. $\newline$ Median of new data set: $51$

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