Question 10 :

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:

here we have to consider the first data that is time as (x) and no of people as (f). Since the time is in the form of interval we have to find the mid value and take it as x.

 x f d = x-17.5 d² fd² 7.5 4 7.5-17.5=10 100 400 12.5 8 12.5-17.5=-5 25 200 17.5 15 17.5-17.5=0 0 0 22.5 12 22.5-17.5=5 25 300 27.5 11 27.5-17.5=10 100 1100 Σ f = 50 Σfd²=2000

σ   = √(Σfd²/Σf)

=  √(2000/50)

= √40

= 6.32

Question 11 :

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:

here we have to consider the first data that is amount as (x) and no of horse as (f). Since the amount is in the form of interval we have to find the mid value and take it as x.

 x f d=x- 50 d² fd² 10 2 10-20=-10 100 200 30 7 30-50=-20 400 2800 50 12 50-50=0 0 0 70 19 70-50=20 400 7600 90 5 90-50=40 1600 8000 Σ f = 45 Σfd²=18600

σ   = √(Σfd²/Σf)

=  √(18600/45)

= √413.34

= 20.33

Question 12:

Find the variance of the following distribution

Class interval      20-24     25-29     30-34     35-39     40-44     45-59

Frequency             15          25          28           12        12        8

calculate the standard deviation.

Solution:

here we have to consider the first data that is class interval as (x) and no of frequency as (f).

 x f d=x- 32 d² fd² 22 15 22-32=-10 100 1500 27 25 27-32=-5 25 625 32 28 32-32=0 0 0 37 12 37-32=5 25 300 42 12 42-32=10 100 1200 47 8 47-32=15 225 1800 Σ f = 100 Σfd²=5425

σ   = √(Σfd²/Σf)

=  √(5425/100)

= √54.25

= 7.37  