Question

(b) mean = 37, median = 40, standard deviation = 4
the coefficient of skewness is .
this distribution is select.

Explanation:

Step1: Recall skewness formula

The formula for the coefficient of skewness (using the relationship between mean, median and standard - deviation) is $Sk=\frac{3(\bar{x}-M)}{s}$, where $\bar{x}$ is the mean, $M$ is the median and $s$ is the standard deviation.

Step2: Substitute given values

Given $\bar{x} = 37$, $M = 40$, and $s = 4$. Substitute into the formula: $Sk=\frac{3(37 - 40)}{4}$.

Step3: Calculate the numerator

First, calculate $37-40=-3$. Then $3\times(-3)= - 9$.

Step4: Calculate the coefficient of skewness

$Sk=\frac{-9}{4}=-2.25$.

Step5: Determine the type of distribution

If $Sk < 0$, the distribution is negatively skewed.

Answer:

The coefficient of skewness is $-2.25$. This distribution is negatively skewed.