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Question

From the prices of shares X and Y below find out which is more stable in value :
X35545253565852505149
Y108107105105106107104103104101

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Solution


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
Total= 510
Here, the number of observations n=10
Mean,¯X=1n10i=1Xi=110×510=51
Variance(σ21)=1n10i=1(Xi¯X)2
=110×350=35
Standard deviation (σ1)=35=5.91
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
101 416
Total= 1050 40
Here, the number of observations n=10
Mean,¯Y=1n10i=1Yi=110×1050=105
Variance(σ22)=1n10i=1(Yi¯Y)2
=110×40=4
Standard deviation (σ2)=4=2

Since, the variance of prices of share X is greater than that of prices of share Y.
So, prices of share X are more variable than prices of share Y.
So, the prices of shares Y are more stable than the prices of share X.

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