In this page 10th grade statistics solution4 we are going to see solution of some practice questions of 10th grade statistics worksheet1.
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
10th grade statistics solution4 10th grade statistics solution4
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