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Look at this set of $6$ numbers: $\newline$ $45, 53, 53, 41, 36, 33$ $\newline$ 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

6

numbers:

\newline

45, 53, 53, 41, 36, 33

\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 Data in Order: Arrange the original data set in ascending order. $\newline$ Data set in order: $33, 36, 41, 45, 53, 53$ .
Calculate Original Median: Calculate the median of the original data set. $\newline$ Since there are $6$ numbers, the median is the average of the $3$ rd and $4$ th numbers: $(41 + 45) / 2 = 43$ .
Add Number $43$ : Add the number $43$ to the data set and arrange it in ascending order. $\newline$ New data set: $33, 36, 41, 43, 45, 53, 53$ .
Calculate New Median: Calculate the median of the new data set. $\newline$ With $7$ numbers, the median is now the $4$ th number, which is $43$ .
Compare Medians: Compare the original median to the new median. Original median: $43$ , New median: $43$ . There is no change in the median.

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