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Look at this set of $10$ numbers: $\newline$ $46, 72, 34, 76, 75, 38, 60, 15, 79, 70$ $\newline$ How would the median change if the number $43$ 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

10

numbers:

\newline

46, 72, 34, 76, 75, 38, 60, 15, 79, 70

\newline

How would the median change if the number

43

were added to the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Arrange Numbers in Ascending Order: Step $1$ : Arrange the original set of numbers in ascending order. $\newline$ Numbers: $46, 72, 34, 76, 75, 38, 60, 15, 79, 70$ . $\newline$ Ordered set: $15, 34, 38, 46, 60, 70, 72, 75, 76, 79$ .
Find Median of Original Set: Step $2$ : Find the median of the original set. $\newline$ Since there are $10$ numbers, the median is the average of the $5$ th and $6$ th numbers. $\newline$ Median = $(60 + 70) / 2 = 65$ .
Add Number $43$ and Reorder: Step $3$ : Add the number $43$ to the set and reorder it. $\newline$ New set: $15, 34, 38, 43, 46, 60, 70, 72, 75, 76, 79$ .
Find Median of New Set: Step $4$ : Find the median of the new set. $\newline$ With $11$ numbers, the median is now the $6$ th number. $\newline$ New median = $60$ .

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