Question

Find the mean deviation

Marks: 0-10 10-20 20-30 30-40

No. of workers: 6 5 8 15

Marks: 40-50 50-60 60-70

No. of workers: 7 6 3​

Answer 1

$\fbox{ANSWER}\\\\ \underline{Given:}\\X Mid Point (X) Frequency (F) i=class interval width A=45 Assumed mean d'= ix−A​ fd$

$\huge{To find :}$

0-10 5  3  10  45  -4  -12  

10-20  15  5  10  45  -3  -15

20-30  25  6  10  45  -2  -12  

30-40  35  7  10  45  -1  -7  

40-50  45=A 8  10  45  0  0  

50-60  55  9  10  45  1  9  

60-70  65  10  10  45  2  20  

70-80  75  12  10  45  3  36  

80-90  85  6  10  45  4  24  

90-100   95 4  10  45  5  20  

$\textit{Solution:}$

The formula used for arithmetic mean of grouped data by step deviation method is,  

X

=A+  

∑f

∑fd  

′

 

​  

×i  

A= Assumed mean of the given data

∑ = Summation of the frequencies given in the grouped data

∑fd  

′

 = Summation of the frequencies and deviation of a given mean data

d  

′

=  

i

(x−A)

​  

$\huge{ARMETHIC FORMULA :}$

 

i= Class interval width

X

 = arithmetic mean

X

=45+  

70

63

​  

×10

=45+9

=54