Question

Heights of the students in a class are given in the distribution below:

5' - 5'2"      10

5'2" - 5'4" 40

5'4" - 5'6"   25 .

Find:

1. Skewness and Kurtosis

Answer 1

$Mean=\frac{∑fx}{n}=\frac{400.5}{75}=5.34$

Sample standard deviation, $s=\sqrt{\frac{f∑(x-5.34)^2}{n-1}}=\sqrt{\frac{1.28}{74}}=0.1315$

Skewness $=\frac{f∑(x-5.34)^3}{(n-1)*s^3}=\frac{-0.0384}{74*(0.1315)^3}=-0.2282$

Kurtosis $=\frac{f∑(x-5.34)^4}{(n-1)*s^4}=\frac{0.0497}{74*(0.1315)^4}=2.2461$