## 10th Grade Statistics Solution3

In this page 10th grade statistics solution3 we are going to see solution of some practice questions of 10th grade statistics worksheet1.

Question 7 :

Calculate the standard deviation of the following data

x     3     8    13    18    23

7    10    15    10    8

Solution:

Since these are grouped data we don't have to write them as ascending order.

Let us use actual mean method to find standard deviation.

 x f d = x - 13 d² fd² 3 7 3 - 13 = -10 100 700 8 10 8 - 13 = -5 25 250 13 15 13 - 13 = 0 0 0 18 10 18 - 13 = 5 25 250 23 8 23 - 13 = 10 100 800 Σ f = 50 Σfd²=2000

σ  = √(Σfd²/Σf)

=  √(2000/50)

= √40

= 6.32455

= 6.32

Question 8 :

The number of books bought at a book fair 200 students from a school are given in the following table.

Number of books           0       1        2       3        4

Number of students       35     64       68     18       15

calculate the standard deviation.

Solution:

 x f d = x - 2 d² fd² 0 35 0 - 2 = -2 4 140 1 64 1 - 2 = -1 1 64 2 68 2 - 2 = 0 0 0 3 18 3 - 2 = 1 1 18 4 15 4 - 2 = 2 4 60 Σ f = 200 Σfd²=282

σ  = √(Σfd²/Σf)

=  √(282/200)

= √1.41

= 1.18

10th grade statistics solution3 10th grade statistics solution3

Question 9:

Calculate the variance of the following table.

x    2    4    6     8    10    12    14    16

f    4    4    5    15     8      5      4    5

Solution:

 x f d = x - 8 d² fd² 2 4 2 - 8 = -6 36 144 4 4 4 - 8 = -4 16 64 6 5 6 - 8 = -2 4 20 8 15 8 - 8 = 0 0 0 10 8 10 - 8 = 2 4 32 12 5 12 - 8 = 4 16 80 14 4 14 - 8 = 6 36 144 16 5 16 - 8 = 8 64 320 Σ f = 50 Σfd²=804

σ²  = √(Σfd²/Σf)

=  √(804/50)

= 16.08  