Find the mean deviation for the following data, 46, 34, 22, 26, 14, 20, 16, and 44.

CONCEPT:

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 of numbers are 46, 34, 22, 26, 14, 20, 16, and 44.

Mean \(\bar x = \frac{{Sum\;of\;all\;the\;observations}}{{Total\;number\;of\;observations}} = \frac{{46\; +\; 34\; + \;22\; + \;26\; + \;14\; + \;20\; + \;16\; + \;44}}{8} = 27.75\)

∴ Mean deviation \( = \frac{{\left| {46 - 27.75} \right| + \left| {34 - 27.75} \right| + \left| {22 - 27.75} \right| + \left| {26 - 27.75} \right| + \left| {14 - 27.75} \right| + \left| {20 - 27.75} \right| + \left| {16 - 27.75} \right| + \left| {44 - 27.75} \right|}}{8}\) 

⇒ Mean deviation = \(\frac{{81.5}}{8} \) = 10.18