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Look at this set of $6$ numbers: $\newline$ $49, 12, 15, 69, 15, 31$ $\newline$ How would the median change if the number $43$ replaced the number $12$ 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

6

numbers:

\newline

49, 12, 15, 69, 15, 31

\newline

How would the median change if the number

43

replaced the number

12

in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Arrange Numbers Ascending: Step $1$ : Arrange the original set of numbers in ascending order. $\newline$ Original set: $49, 12, 15, 69, 15, 31$ $\newline$ Ascending order: $12, 15, 15, 31, 49, 69$
Find Original Set Median: Step $2$ : 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. $\newline$ Median = $(15 + 31) / 2 = 23$
Replace Number with $43$ : Step $3$ : Replace the number $12$ with $43$ in the set and arrange it in ascending order. $\newline$ New set: $49, 43, 15, 69, 15, 31$ $\newline$ Ascending order: $15, 15, 31, 43, 49, 69$
Find New Set Median: Step $4$ : Find the median of the new set. $\newline$ Since there are still $6$ numbers, the median is the average of the $3$ rd and $4$ th numbers. $\newline$ Median $= (31 + 43) / 2 = 37$

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