Question

Calculate the standard deviations of the following

Marks 0-10 10-20 20-30 30-40 40-50

Number of students 7 12 18 42 48​

Answer 1

X Mid Point (X)  Frequency (F)  i=class interval width  A=45 Assumed mean  u=  

i

x−A

​  

  fu  

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  

   Σf=70        Σfu=63  

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

X

=A+  

∑f

∑fu

​  

×i  

A= Assumed mean of the given data

∑ = Summation of the frequencies given in the grouped data

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

u=  

i

(x−A)

​  

 

i= Class interval width

X

 = arithmetic mean

X

=45+  

70

63

​  

×10

=45+9

=54