Statistics – Exercise 6.1 – Class X

Statistics – Exercise 6.1

Solve the following using step deviation of the following data.

  1. Calculate the standard deviation of the following data.
x38131823
f71015108

 

  1. The number of books bought by 200 students in a book exhibition is given below.
No. of books01234
No. of students3564681815

Find the variance and standard variation.

  1. The marks scored by 60 students in a science test are gven below.
Marks(x)102030405060
No. of students812201073

Calculate the variance and standard deviation

  1. The daily wages of Rs. 40 workers of a factory are given in the following table.
Wages in Rs.30 – 3434 – 3838 – 4242 – 4646 – 5050 – 54
No. of workers4791163

Calculate (i) Mean (ii) variance and (iii) standard deviation of wages and interpret the findings

  1. Mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and the sum of squares of all the items.
  2. In study of diabetic patients in a village, the following observations were noted.
Age in years10 – 2020 – 3030 – 4040 – 5050 – 6060 – 70
No. of patients25121993

Calculate the mean and standard deviation. Also interpret the results.


Statistics – Exercise 6.1 – Solution

Solve the following using step deviation of the following data.

  1. Calculate the standard deviation of the following data.
x38131823
f71015108

Solution:

Let the assumed mean, A = 13

The common factor of the scores, C = 5

xfStep deviation
d = x-A/C
fdd2fd2
37-2-14428
810-1-10110
13150000
1810110110
238216432
n = 50⅀fd = 2⅀fd2 = 80

1

Therefore standard deviation is 6.32


  1. The number of books bought by 200 students in a book exhibition is given below.
No. of books01234
No. of students3564681815

Find the variance and standard variation.

Solution:

Let the assumed mean, A = 2

The common factor of the scores, C = 1

No. of booksNo. of studentsStandard deviation, d= x-A/Cfdd2fd2
035-2-704140
164-1-64164
2680000
318118118
415230460
⅀f = 200⅀fd = -86⅀d2 = 10⅀fd2 = 282

2

Therefore, standard deviation is 1.107 and variance is 1.23


  1. The marks scored by 60 students in a science test are gven below.
Marks(x)102030405060
No. of students812201073

Calculate the variance and standard deviation.

Solution:

Let assumed mean , A = 40

C = 10

Marks(x)No. of studentsdfdd2fd2
108-3-24972
2012-2-24448
3020-1-20120
40100000
5071717
60326412
n = 60⅀d = -3⅀fd = -55⅀fd2 = 159

3

Therefore, standard deviation is 13.4 and variance is 179.23


  1. The daily wages of Rs. 40 workers of a factory are given in the following table.
Wages in Rs.30 – 3434 – 3838 – 4242 – 4646 – 5050 – 54
No. of workers4791163

Calculate (i) Mean (ii) variance and (iii) standard deviation of wages and interpret the findings

Solution:

Assumed  mean, A = 40

C = 34 – 30 = 4

Wages in Rs.No. of workers(f)xfxd = x-A/Cfdd2fd2
30 – 34432128-2-8416
34 – 38736252-1-717
38 – 429403600000
42 – 461144484111111
46 – 50648288212424
50 – 5435215639927
n = 40⅀fx = 1668⅀fd  =  17⅀fd2 = 85

4

This means each score deviates from the mean value 41.7 by 5.58


5. Mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and the sum of squares of all the items.

Solution:

The number of items  = n = 100

Mean of 100 items = 48

Standard deviation, = 10

Sum of scores ,

Standard deviation of 100 items, = 10

Statistics – Exercise 6.1 – Class X

Therefore, sum of all the items is 4800 and the sum of squares of all the items is 2,40,400


  1. In study of diabetic patients in a village, the following observations were noted.
Age in years10 – 2020 – 3030 – 4040 – 5050 – 6060 – 70
No. of patients25121993

Calculate the mean and standard deviation. Also interpret the results.

Solution:

Assumed mean A = 35

C = 10

Age in yearsNo. of patientsxfxd =

x-A/C

 

d2fdfd2
10 – 2021530-24-48
20 – 3052550-11-55
30 – 4012354200000
40 – 501945855111919
50 – 60955495241836
60 – 7036519539927
n = 50⅀fx = 2045⅀fd = 37⅀fd2 = 95

 

Statistics – Exercise 6.1 – Class X

This means each score deviates from the mean value 41.7 by 11.62


Next exercise – Statistics – Exercise 6.2 – Class X