SaiBook.us Statistics

Example

Title: Karl pearson’s coefficient of skewness

Grade: 9-a Lesson: S2-L7

Explanation: The best way to understand statistics is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

Calculate Karl person’s coeffiecient of skewness for the following data:28,23,18,28,26,43,28,30,26.

Step 1a

Calculate the Mean,Mode

Explanation:

Mean = \$"sum of observations"/"number of observations"\$

Sum of observations = 28+23+18+28+26+43+28+30+26 = 250

Number of observations = 9

Mean = \$250/9\$

Mean = 27.78

Mode = most common number in the observations

Mode = 28

Step 1b

Calculate the standard deviation

Explanation:

Standard deviation = \$\sqrt((\sum x^2/n) - (\barx)^2)\$

\$\sum x^2\$ = \$28^2 +23^2 +18^2 +28^2 +26^2 +43^2 +28^2 +30^2 +26\$

\$\sum x^2\$ = 7306

Mean \$\barx\$ = 27.78

Standard deviation = \$\sqrt(7306/9 - (27.78)^2)\$

Standard deviation = \$\sqrt 40.04\$

Standard deviation = 6.3285

Step 1c

Calculate Skewness

Explanation:

Skewness = \$(Mean-Mode)/ "S.D."\$

Skewness = \$(27.78-28)/ 6.3285\$

Skewness = -0.0348

\$S_k\$< 0 i.e,negatively skewed.