## FIND STANDRAD DEVIATION FOR UNGROUPED DATA

Question 1 :

Calculate the standard deviation of the following data.

38, 40, 34, 31, 28, 26, 34

Solution :

First write the given data in the ascending order.

26, 28, 31, 34, 34, 38, 40

x̄  =  Σx/n

=  (26+28+31+34+34+38+40)/7

=  231/7

=  33

 x26283134343840 d = x -x̄ and d = x - 3326-33  =  -728-33  =  -531-33  =  -234-33  =  134-33  =  138-33  =  540-33  =  7 d249254112549Σd2  =  154

σ  =  √(Σd²/n)

=  √(154/7)

=  √22

=  4.690

=  4.69

So, standard deviation of the given data is 4.69.

Question 2 :

Calculate the standard deviation of the following data

x     3     8    13    18    23

7    10    15    10    8

Solution :

Let us use actual mean method to find standard deviation.

 x38131823 f71015108 d = x - 13-10-50510 d²10025025100 fd²7002500250800

Σf  =  50 and Σfd²  =  200

σ  =  √(Σfd²/Σf)

=  √(2000/50)

=  √40

=  6.32455

=  6.32

So, standard deviation of the given data is 6.32

Question 3 :

The number of books bought at a book fair 200 students from a school are given in the following table.

Number of books              0       1        2       3        4

Number of students       35     64       68     18       15

calculate the standard deviation.

Solution :

 x01234 f356468185 d = x - 2-2-1012 d²41014 fd²1406401860

σ  =  √(Σfd²/Σf)

=  √(282/200)

=  √1.41

=  1.18

So, standard deviation of the given data is 1.18

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