From the prices of shares of X and Y below, find out which is more stable in value:
x    35    54    52    53    56    58    52    50    51    49
y   108  107 105   105  106  107  104  103  104  101

Solution:

The prices of the shares X are

35, 54, 52, 53, 56, 58, 52, 50, 51, 49

Here, the number of observations, N = 10

Mean,

x = 1/N ∑¹⁰_{i = 1}x_i

= 1/10 x 510

= 51

The following table is obtained corresponding to shares X.

xi	(xi - x)	(xi - x)2
35	-16	256
54	3	9
52	1	1
53	2	4
56	5	25
58	7	49
52	1	1
50	- 1	1
51	0	0
49	- 2	4
		350

Variance,

(σ₁²) = 1/N [N ∑¹⁰_{i = 1}(x_i - x)

= 1/10 × 350

= 35

Standard deviation,

(σ₁) = √35

= 5.91

C.V.(Shares X) = σ₁/X × 100

= 5.91/51 × 100

= 11.58

The prices of the shares Y are

108, 107, 105, 105, 106, 107, 104, 103, 104, 101

Here, the number of observations, N = 10

Mean

y = 1/N ∑¹⁰_{i = 1}y_i

= 1/10 x 1050

= 105

The following table is obtained corresponding to shares Y.

yi	(yi - y)	(yi - y)²
108	3	9
107	2	4
105	0	0
105	0	0
106	1	1
107	2	4
104	- 1	1
103	- 2	4
104	- 1	1
101	- 4	16
		40

Variance,

(σ₂²) = 1/N [N ∑¹⁰_{i = 1}(y_i - y)

= 1/10 × 40

= 4

Standard deviation,

(σ₂) = √4

= 2

C.V.(Shares X) = σ₂/X × 100

= 2/105 × 100

= 1.9

C.V. of prices of shares X is greater than the C.V of prices of shares Y.

Thus, the prices of shares Y are more stable than the prices of shares X

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NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.3 Question 2

From the prices of shares of X and Y below, find out which is more stable in value:

Summary:

From the given data, the prices of shares Y are more stable than the prices of shares X