10th Grade Statistics Solution4

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

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





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





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


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