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Look at this set of $6$ numbers: $\newline$ $3, 4, 8, 9, 8, 3$ $\newline$ How would the median change if the number $6$ 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

6

numbers:

\newline

3, 4, 8, 9, 8, 3

\newline

How would the median change if the number

6

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 set: $3, 3, 4, 8, 8, 9$
Find Original Set Median: Find the median of the original set. $\newline$ Since there are $6$ numbers, the median is the average of the $3$ rd and $4$ th numbers: $(4 + 8) / 2 = 6$ .
Add Number $6$ and Rearrange: Add the number $6$ to the original set and arrange it. $\newline$ New set: $3, 3, 4, 6, 8, 8, 9$
Find New Set Median: Find the median of the new set. $\newline$ With $7$ numbers, the median is now the $4$ th number, which is $6$ .

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