Question

From the following distribution, calculate mean deviation about mean
$\begin{tabular}{|l|c|c|c|c|c|} Marks & 10 & 20 & 30 & 40 & 50 \\ No. of Students & 5 & 7 & 15 & 13 & 10 \end{tabular}$

Answer 1

To find the mean deviation,first calculate the mean of the given distribution

$\begin{table}[] \begin{tabular}{|l|l|l|l|l|} \cline{1-5} x_{i} & \begin{tabular}[c]{@{}l@{}}Frequency\\ f_{i}\end{tabular} & (x_{i}f_{i})& | x_{i}-33.2| & f_{i}|x_{i}-\bar x| \\ \cline{1-5} 10 & 5 & 50 & 23.2 & 116 \\ \cline{1-5} 20 & 7 & 140 & 13.2 & 92.4 \\ \cline{1-5} 30 & 15 & 450 & 3.2 & 48 \\\cline{1-5} 40 & 13 & 520 & 6.8 & 88.4 \\ \cline{1-5} 50 & 10 & 500 & 16.8 & 168 \\\cline{1-5} Total & 50 & 1660 & & 512.2 \\ \cline{1-5} \end{tabular} \end{table}$

$N = \Sigma \: f = 5 + 7 + 15 + 13 + 10 \\ \\ = 50 \\ \\ \bar x = \frac{1660}{50} = 33.2$

Mean Deviation about mean

$MD(\bar x) = \frac{\Sigma \: f_{i} |x_{i} - \bar x| }{N} \\ \\ = \frac{512.2}{50} \\ \\ =10.256$

Hence mean deviation about mean is 10.256
Hope it helps you