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

x

26

28

31

34

34

38

40

d = x -x̄ and d = x - 33

26-33  =  -7

28-33  =  -5

31-33  =  -2

34-33  =  1

34-33  =  1

38-33  =  5

40-33  =  7

d2

49

25

4

1

1

25

49

Σd =  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.

x

3

8

13

18

23

f

7

10

15

10

8

d = x - 13

-10

-5

0

5

10

100

25

0

25

100

fd²

700

250

0

250

800

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 :

x

0

1

2

3

4

f

35

64

68

18

5

d = x - 2

-2

-1

0

1

2

4

1

0

1

4

fd²

140

64

0

18

60

σ  =  √(Σfd²/Σf)

=  √(282/200)

=  √1.41

=  1.18

So, standard deviation of the given data is 1.18

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