Question

Calculate mean deviation from mean for the following frequency array.​

Answer 1

Answer:

Mean deviation about mean of the given data is 10.67

Step-by-step explanation:

Given data,

$\boxed{\begin{array} {c|c}\bf x &\bf Frequency \\\cline{1-2}10&8\\20&12\\30&20\\40&10\\50&6\\60&4\end{array}}$

Mean deviation about mean is given by $\sf\dfrac{\sum f|x_i - \overline{x}|}{\sum f}$. Therefore, we have to find the mean of the given data first.

Mean is given by,

$\sf\overline{x} = \dfrac{\sum x_if_i}{\sum f_i}$

From the given data, we will find $\sf\sum x_i f_i$

$\boxed{\begin{array} {c|c|c}\bf X &\bf F & \bf XF\\\cline{1-3}10&8 & 80\\20&12& 240\\30&20&600\\40&10&400\\50&6&300\\60&4&240\\\cline{1-3}\bf Total & 60&1860\end{array}}$

Therefore, mean is given by,

$\implies \sf\overline{x} = \dfrac{\sum x_if_i}{\sum f_i}$

$\implies \sf\overline{x} = \dfrac{1860}{60}$

$\implies \sf\overline{x} = 31$

Now we have to find $\sf\sum f |x_i - \overline{x}|$ in order to find mean deviation about mean.

$\boxed{\begin{array} {c|c|c}\bf x &\bf f & \bf f|x-\overline{x} | \\\cline{1-3}10&8 & 168\\20&12& 132\\30&20&20\\40&10&90\\50&6&114\\60&4&116\\\cline{1-3}\bf Total & 60&640\end{array}}$

So the mean deviation is given by:

$\textbf{\textsf{Mean deviation = \sf\dfrac{\sum f|x_i - \overline{x}|}{\sum f} }}$

$\textbf{\textsf{Mean deviation = \sf\dfrac{640}{60} }}$

$\textbf{\textsf{Mean deviation =10.67 }}$

This is the required answer.