Question

Count: 100
Mean: 83.59
Median:93
Standard deviation: 22.26
IQR:17
Q1:80
Q3:97
a) Which is better summary of the percentage of white residents in the neighborhood, the mean or median.
b) Which is a better summary of the spread, the IQR or the standard deviation? Explain.

Answer 1

Answer on Question #54883 – Math – Statistics and Probability

Count: 100

Mean: 83.59

Median: 93

Standard deviation: 22.26

IQR: 17

Q1: 80

Q3: 97

a) Which is better summary of the percentage of white residents in the neighborhood, the mean or median?

b) Which is a better summary of the spread, the IQR or the standard deviation? Explain.

Solution

Pearson's skewness coefficient is

$$\frac {3 (\text{Mean} - \text{Median})}{\text{Standard deviation}} = \frac {3 (83.59 - 93)}{22.26} = -1.268.$$

a) A better summary of the percentage of white residents in the neighborhood is Median, because the distribution is so skewed to the left.

b) A better summary of the spread is IQR, because the distribution is skewed.

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