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Look at this set of $6$ numbers: $\newline$ $93, 81, 83, 83, 43, 22$ $\newline$ How would the median change if the number $24$ replaced one of the $83$ 's in the set? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease $\newline$ (C)no change $\newline$

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Changes in mean, median, mode, and range

Full solution

Q. Look at this set of

6

numbers:

\newline

93, 81, 83, 83, 43, 22

\newline

How would the median change if the number

24

replaced one of the

83

's in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

\newline

Identify and Arrange Original Set: Identify the original set and arrange it in ascending order. $\newline$ Original set: $93, 81, 83, 83, 43, 22$ $\newline$ Sorted set: $22, 43, 81, 83, 83, 93$
Calculate Median of Original Set: Calculate 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. $\newline$ Median = $(81 + 83) / 2 = 82$
Replace and Sort New Set: Replace one of the $83$ 's with $24$ and sort the new set. $\newline$ New set: $93$ , $81$ , $24$ , $83$ , $43$ , $22$ $\newline$ Sorted new set: $22$ , $24$ , $43$ , $81$ , $83$ , $93$
Calculate Median of New Set: Calculate the median of the new set. Median = $(43 + 81) / 2 = 62$

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