In this page 10th grade statistics solution2 we are going to see
solution of some practice questions of 10th grade statistics worksheet1.

Question 3:

The largest of 50 measurements is 3.84 kg. If the
range is 0.46 kg ,find the smallest
measurement.

Solution:

L = 3.84 R = 0.46

R = L – S

0.46 = 3.84 – S

S = 3.84 – 0.46

S = 3.38 kg

Question 4:

The standard deviation of 20 observations is √5.
If each observation is multiplied by 2,find the standard deviation and variance
of the resulting observations.

Solution:

Here √5 is the standard deviation of 20 observations. Now we
need to find the standard deviation and variance if each observation is
multiplied by 2.

Standard deviation (σ) = 2 √5

Question 5:

Calculate the standard deviation of the first 13 natural
numbers.

Solution:

Formula:

= √(n²
-1)/12

= √(13²
-1)/12

= √(169
-1)/12

= √168/12

= √14

= 3.7416

= 3.74

Therefore the standard deviation for first 13 numbers is 3.74

Question 6 :

Calculate the standard deviation
of the following data

(i) 10,20,15,8,3,4

Solution:

First we have to write the given data
in the ascending order.

3,4,8,10,15,20

Since the given numbers are small we can use direct method to find standard deviation.

x

x²

3

9

4

16

8

64

10

100

15

225

20

400

Σ x = 60

Σ x² = 814

σ = √(Σ x²/n) - (Σ x/n)²

= √(814/6) - (60/6)²

= √[135.67 - (10)²]

= √(135.67 - 100)

= √35.67

= 5.97

(ii) 38,40,34,31,28,26,34

Solution:

First we have to write the given data
in the ascending order.

26,28,31,34,34,38,40

Since the given numbers are little large we can use actual mean method to find standard deviation.