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Look at this set of $7$ numbers: $\newline$ $8, 2, 9, 9, 1, 6, 7$ $\newline$ How would the median change if the number $1$ replaced one of the $9$ '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

8, 2, 9, 9, 1, 6, 7

\newline

How would the median change if the number

1

replaced one of the

9

'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: $1, 2, 6, 7, 8, 9, 9$ .
Identify Median: Identify the median of the original set. $\newline$ The median is the middle value, so for the original set, the median is $7$ .
Replace and Rearrange: Replace one of the $9$ 's with a $1$ and rearrange the set. $\newline$ New set: $1, 1, 2, 6, 7, 8, 9$ .
Find New Median: Find the median of the new set. $\newline$ The middle value of the new set is still $7$ .

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