Correct Answer - Option 1 : 14.7
Given:
36, 65, 38, 80, 42, 67, 33, 53, 76, 45
Formula used:
Median = {(n + 1)/2}th term when total number of observation given is odd
Median = [(n/2)th term + {(n/2) +1}th term]/2 when total number of observation given is even
\({\rm{M}}.{\rm{D}} = \frac{{∑ \left| {{\rm{X}} - {\rm{M}}} \right|}}{{\rm{N}}}\)
Where
M.D = mean deviation about median
∑ = summation
X = observations or values
M = median
N = number of observations
Calculation:
At first, we have to rearrange the numbers in ascending order.
⇒ 33, 36, 38, 42, 45, 53, 65, 67, 76, 80
Here number of observations are 10
Median = (5th term + 6th term)/2
⇒ (45 + 53)/2
⇒ 98/2
⇒ 49
\({\rm{M}}.{\rm{D}} = \frac{{\left| {\left( {33 - 49} \right)|\; + \left|( {36 - 49} \right)| + \left|( {38 - 49} \right)| + \left|( {42\; - \;49} \right)|\; + \left|( {45\; - 49} \right)| + \left|( {53\; - \;49} \right)| + \left|( {65\; - 49} \right)| + \left|( {67\; - \;49} \right)| + \left|( {76\; - \;49} \right)| +\left|( {80\; - \;49} \right)} \right|}}{{10}}\)
⇒ \(\frac{{\left( {16 + \;13 + 11 + 7 + 4 + 4 + 16 + 18 + 27 + 31} \right)\;}}{{10}}\)
⇒ 147/10
⇒ 14.7
∴ The mean deviation about the Median of the distribution is 14.7
