Standard Deviation

Statistics : Standard Deviation continued

Formula to find the Standard Deviation of a Frequency Distribution

 $S.D.\ =\sqrt{\frac{\in\left(x-\overline{x}\right)^2f}{\in f}}where\ \overline{x}\ =\frac{\in xf}{\in f}$  

The first 2 columns are given to you. ( x and f)

The table below shows the distribution of marks in an examination. Calculate the S.D of this set of data.

 $\overline{x}\ =\frac{\in xf}{\in f}=\frac{300}{60}=5$  
 $S.D.\ =\sqrt{\frac{\in\left(x-\overline{x}\right)^2f}{\in f}\ }=\sqrt{\frac{292}{60}}=2.21$  
The data is relatively normal.

Standard Deviation for Grouped Data.

The frequency table below shows the distribution of heights of 100 students at a school. Find the S.D of this data.

 $\overline{x}\ =\frac{\in fx}{\in f}=\frac{15870}{100}=158.7$  

 $S.D.=\ \sqrt{\frac{\in\left(x-\overline{x}\right)^2f}{\in f}}=\sqrt{\frac{7161}{100}}=8.46$