SaiBook.us Statistics

Example

Title: Kurtosis

Grade: 9-a Lesson: S2-L9

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

Examples:

Consider the following set of ungrouped data values, 23,34,38,47,59,63,84.

Step 1a

Calculate the mean

Explanation:

\$\barx = \sumx_i/n\$

\$\barx = (23+34+38+47+59+63+84)/7 \$

\$\barx = 348/7\$

\$\barx = 49.71\$

$1$

Step 1b

Calculating the standard deviation

Explanation:

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

\$\sigma = \sqrt(2543.3/7)\$

\$\sigma = 19.06\$

Step 1c

Calculate Kurtosis

Explanation:

Kurtosis = \$(\sum(x_i - \barx)^4)/(n×\sigma^4)\$

substitute \$\sum(x_i - \barx)^4 = 2009579,n = 7,\sigma = 19.06\$ in kurtosis

Kurtosis = \$2009579/(7×19.06^4)\$

Kurtosis = 2.17