## 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.

 x7.512.517.522.527.5 f48151211 d = x-17.57.5-17.5=1012.5-17.5=517.5-17.5=022.5-17.5=527.5-17.5=10 d210025025100 fd240020003001100

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.

 x1030507090 f2712195 d = x-5010-50 = -4030-50 = -2050-50 = 070-50 = 2090-50 = 40 d2160040004001600 fd232002800076008000

Σf  =  45 and Σfd²  =  21600

σ  =  √(Σfd²/Σf)

=  √(21600/45)

=  √480

=  21.90

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