STANDARD DEVIATION FORM FREQUENCY TABLE WITH INTERVALS

Question 1 :

The time (in seconds) taken by a group of people to walk across a pedestrian crossing is given in the table below.

Time (in sec)   5-10      10-15      15-20      20-25     25-30

No of people       4             8           15           12         11

Calculate the standard deviation.

Solution :

x - time taken by a group of people and f - number of people.

x

7.5

12.5

17.5

22.5

27.5

f

4

8

15

12

11

d = x-17.5

7.5-17.5=10

12.5-17.5=5

17.5-17.5=0

22.5-17.5=5

27.5-17.5=10

d2

100

25

0

25

100

fd2

400

200

0

300

1100

Σf  =  50 and Σfd²  =  2000

σ  =  √(Σfd²/Σf)

=  √(2000/50)

=  √40

=  6.32

Question 2 :

A group of 45 house owners contributed money towards green environment of their street. The amount of money collected is shown in the table below.

Amount          0-20   20-40   40-60    60-80    80-100

No of house      2         7          12          19           5 

Calculate the standard deviation.

Solution :

x-Amount of money collected and f - number of houses.

x

10

30

50

70

90

f

2

7

12

19

5

d = x-50

10-50 = -40

30-50 = -20

50-50 = 0

70-50 = 20

90-50 = 40

d2

1600

400

0

400

1600

fd2

3200

2800

0

7600

8000

Σf  =  45 and Σfd²  =  21600

σ  =  √(Σfd²/Σf)

=  √(21600/45)

=  √480

=  21.90

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