Question

Given the box plot, will the mean or the median provide a better description of the center?

box plot with min at 6, Q1 at 7.5, median at 8, Q3 at 23, max at 32.5

The mean, because the data distribution is symmetrical
The median, because the data distribution is symmetrical
The mean, because the data distribution is skewed to the right
The median, because the data distribution is skewed to the right

Answer 1

Last one:

The median, because the data distribution is skewed to the right

Explanation:

Q1: 7.5

Q2: 8

Q3: 23

Q2 - Q1 = 8 - 7.5 = 0.5

Q3 - Q2 = 23 - 8 = 15

Since Q3 - Q2 > Q2 - Q1,

data is positively (right) skewed

Skeweness occurs because of outliers therefore mean is not a suitable option. Median will provide a better description of the centre

Answer 2

The median, because the data distribution is skewed to the right

Explanation:

If the longer part of the box is to the right (or above) the median, the data is said to be skewed right. If the longer part is to the left (or below) the median, the data is skewed left. The data is skewed right. The median would be a better estimate, because one or two numbers on the high end will cause the numbers to be skewed to the right, and the mean to be high