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Look at this set of $6$ numbers: $\newline$ $9, 9, 9, 7, 4, 6$ $\newline$ How would the median change if the number $2$ replaced the number $6$ 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

9, 9, 9, 7, 4, 6

\newline

How would the median change if the number

2

replaced the number

6

in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Identify original set: Step $1$ : Identify the original set of numbers and calculate the median. $\newline$ Original set: $9, 9, 9, 7, 4, 6$ $\newline$ Sort the numbers: $4, 6, 7, 9, 9, 9$ $\newline$ Since there are $6$ numbers, the median is the average of the $3$ rd and $4$ th numbers: $(7 + 9)/2 = 8$
Replace number $6$ : Step $2$ : Replace the number $6$ with $2$ in the set and calculate the new median. $\newline$ New set: $9, 9, 9, 7, 4, 2$ $\newline$ Sort the numbers: $2, 4, 7, 9, 9, 9$ $\newline$ The new median is the average of the $3$ rd and $4$ th numbers: $(7 + 9)/2 = 8$
Compare original and new median: Step $3$ : Compare the original median and the new median to determine the change. $\newline$ Original median: $8$ $\newline$ New median: $8$ $\newline$ Since both medians are equal, there is no change in the median.

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