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Statistics — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSStatistics4 Marks
Question
Calculate mean deviation about median age distribution of $100$ persons given below:
Age
16-20
21-25
26-30
31-35
36-40
41-45
46-50
51-55
No. of persons
5
6
12
14
26
12
16
9
✓

Answer

Converting the given data into continuous frequency distribution by subtrading 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval.
Age
$x_i$
$f_i$
Comulativefrequency
$|d_i| = |x_i - 38|$
$f_i|d_i|$
15.5-20.5 18 5 5 20 100
20.5-25.5 23 6 11 15 90
25.5-30.5 28 12 23 10 120
30.5-35.5 33 14 37 5 70
35.5-40.5 38 26 63 0 0
40.5-45.5 43 12 75 5 60
45.5-50.5 48 16 91 10 160
50.5-55.5 53 9 100 15 135
 
 
$\text{N}=\sum\text{f}_\text{i}=100$
 
 
$\sum\text{f}_\text{i}|\text{d}_\text{i}|=735$
clearly, N = 100 $\Rightarrow\frac{\text{N}}{2}=50.$ Cumulative frequency is just greater than $\frac{\text{N}}{2}$ is 63 and the corresponding class is 35.5 - 40.5. l = 35.5, f = 26, h = 5, F = 37
Therefore, $\text{Median}=\text{l}+\frac{\frac{\text{N}}{2}-\text{F}}{\text{f}}\times\text{h}=35.5+\frac{50-37}{26}\times5=38$
$\text{M.D}=\frac{1}{\text{N}}\sum\text{f}_\text{i}|\text{d}_\text{i}|=\frac{735}{100}=7.35$

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