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From the prices of shares X and Y below, find out which is more stable in value:
Class 11 | Exercise 15.3 | Maths | NCERT | Statistics
From the prices of shares X and Y below, find out which is more stable in value:

 

 

Solution:-

From the given data,

draw the table of the given data and append other columns after calculations.

Now calculate Mean for x,

Mean \bar{X}=\sum {{x}_{i}}/n

Where, n = number of terms =510/10

=51

Variance for x= \frac{1}{{{n}^{2}}}\left[ N\sum x_{1}^{2}-{{\left( \sum {{x}_{i}} \right)}^{2}} \right]

=\left( 1/{{10}^{2}} \right)\left[ \left( 10\times 26360 \right)-{{510}^{2}} \right]

=\left( 1/100 \right)\left( 263600-260100 \right)

=3500/100

WKT Standard deviation = \sqrt{\operatorname{var}iance}

=\sqrt{35}

5.91

So, co-efficient of variation =\left( \sigma /\bar{X} \right)\times 100

\left( 5.91/51 \right)\times 100=11.58

Calculate Mean for y,

Mean \bar{Y}=\sum {{Y}_{i}}/N

Where, n = number of terms

=1050/10 =105

Variance for y

=\frac{1}{{{n}^{2}}}\left[ N\sum y_{1}^{2}-{{\left( \sum {{y}_{i}} \right)}^{2}} \right]

\left( 1/{{10}^{2}} \right)\left[ \left( 10\times 110290 \right)-{{1050}^{2}} \right]

=(1/100)(1102900-1102500)

400/100

=4

WKT Standard deviation =\sqrt{\operatorname{var}iance}

=\sqrt{4}

=2

So, co-efficient of variation =\left( \sigma /\bar{X} \right)\times 100

=\left( 2/105 \right)\times 100

1.904

Compare C.V. of X and Y.

C.V of X > C.V. of Y

So, Y is more stable than X.

 

 

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