# From the Prices of Shares X And Y Given Below: Find Out Which is More Stable in Value: X:35545253565852505149y:108107105105106107104103104101 - Mathematics

From the prices of shares X and Y given 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

Let Ax = 51

 $x_i$ $d_i = x_i - 51$ ${d_i}^2$ 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 $\sum d_i = 0$ $\sum d_i^2 = 350$

Here, we have $n = 10, \bar{X} = 51$
$\sigma^2 = \frac{\sum {d_i}^2}{n} - \left( \frac{\sum d_i}{n} \right)^2$
$= \frac{350}{10} - \left( \frac{0}{10} \right)^2$
$= 35 - 0$
$= 35$

$\sigma = \sqrt{35} = 5 . 91$

${CV}_x = \frac{5 . 91}{51} \times 100$
$= 11 . 58$
Let Ay =105
 $x_i$ $d_i = x_i - 105$ ${d_i}^2$ 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 $\sum d_i = 0$ $\sum d_i^2 = 40$

$n = 10, \bar{Y} = 105$
$\sigma^2 = \frac{\sum {d_i}^2}{n} - \left( \frac{\sum d_i}{n} \right)^2$
$= \frac{40}{10} - \left( \frac{0}{10} \right)^2$
$= 4 - 0$
$= 4$

$\sigma = \sqrt{4} = 2$

${CV}_y = \frac{2}{105} \times 100$
$= 1 . 90$

Since CV of prices of share Y is lesser than that of X, prices of shares Y are more stable.

Concept: Statistics - Statistics Concept
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 32 Statistics
Exercise 32.7 | Q 10 | Page 48