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Look at this set of $7$ numbers: $\newline$ $7, 6, 5, 7, 5, 9, 4$ $\newline$ How would the median change if the number $8$ replaced one of the $7$ 's in 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

7

numbers:

\newline

7, 6, 5, 7, 5, 9, 4

\newline

How would the median change if the number

8

replaced one of the

7

's in 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 set: $4, 5, 5, 6, 7, 7, 9$ .
Calculate Original Set Median: Calculate the median of the original set. $\newline$ The median is the middle value, so for the original set, the median is $6$ .
Replace and Rearrange Data: Replace one of the $7$ 's with an $8$ and rearrange the set. $\newline$ New set: $4, 5, 5, 6, 7, 8, 9$ .
Calculate New Set Median: Calculate the median of the new set. $\newline$ The median of the new set is still the middle value, which remains $6$ .

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