Question

lindsey found the median and mean of the list of numbers below:
4, 6, 8, 8, 15
if the number 23 was added to the list, then ______.

a. the median would decrease

b. the median would increase

c. the mean would decrease

d. the mean would increase

Explanation:

Step1: Find original median and mean

Original data: \(4, 6, 8, 8, 15\) (5 numbers).
Median (middle value): \(8\).
Mean: \(\frac{4 + 6 + 8 + 8 + 15}{5}=\frac{41}{5} = 8.2\).

Step2: Find new median and mean (add 23)

New data: \(4, 6, 8, 8, 15, 23\) (6 numbers).
Median (average of 3rd and 4th): \(\frac{8 + 8}{2}=8\) (no change).
Mean: \(\frac{4 + 6 + 8 + 8 + 15 + 23}{6}=\frac{64}{6}\approx10.67\) (increases).

Step3: Analyze options

• A: Median decreases? No (stays 8).
• B: Median increases? No (stays 8).
• C: Mean decreases? No (increases from 8.2 to ~10.67).
• D: Mean increases? Yes.

Answer:

D. the mean would increase