If five friends received their pocket money as 170, 430, 300, 600 and 470 respectively. Find the mean and mean deviation of the received pocket money.

CONCEPT:

• The mean (or average) of a number of observations is the sum of the values of all the observations divided by the total number of observations. It is denoted by the symbol \(\bar x\) , read as ‘x bar’ i.e \(\bar x = \frac{{Sum\;of\;all\;the\;observations}}{{Total\;number\;of\;observations}}\)
• Mean Deviation for ungrouped data:

For ‘n’ observation x₁, x₂………….. x_n, the mean deviation about their mean \(\bar x\) is given by \(M.D = \frac{{\mathop \sum \nolimits_{i = 1}^n \left| {{x_i} - \bar x} \right|}}{N}\) where N is the number of observations.

CALCULATION:

Given data is 170, 430, 300, 600 and 470.

Mean \(\bar x = \frac{{Sum\;of\;all\;the\;observations}}{{Total\;number\;of\;observations}} = \frac{{170\; + \;430 \;+ \;300\; + \;600\; + \;470}}{5} = 394\;\;\)

Mean deviation \(= \frac{{\left| {170 - 394} \right| + \left| {430 - 394} \right| + \left| {300 - 394} \right| + \left| {600 - 394} \right| + \left| {470 - 394} \right|}}{5}\) 

⇒ \(MD= \frac{{636}}{5} = 127.2\)