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Question

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

xi
di=xi-51 di2
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
  di=0 di2=350

Here, we have
n=10, X¯=51σ2=di2n-din2   =35010-0102   =35-0   =35

σ=35=5.91

CVx=5.9151×100        =11.58


Let Ay =105
xi
di=xi-105 di2
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
  di=0 di2=40

n=10, Y¯=105σ2=di2n-din2    =4010-0102    =4-0     =4

σ=4=2

CVy=2105×100        =1.90

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

Mathematics
RD Sharma XI (2015)
Standard XI

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