UPSC NDA I 2025 Mathematics Paper

Given,
The sum and sum of squares of the observations corresponding to length X in cm and weight Y in gm of 50 tropical tubers are given as:
ΣX=200,ΣY=250,ΣX2=900,ΣY2=1400
The formula for variance is:
‌ Variance ‌=‌

ΣX2

N

−(‌

ΣX

N

)2
Where N=50 is the number of observations.
Variance of X :
Variance of X=‌

ΣX2

N

−(‌

ΣX

N

)2
Substituting the given values:
Variance of X=‌

900

50

−(‌

200

50

)2
Variance of X=18−16=2
Variance of Y :
Variance of Y=‌

ΣY2

N

−(‌

ΣY

N

)2
Substituting the given values:
Variance of Y=‌

1400

50

−(‌

250

50

)2
Variance of Y=28−25=3
Conclusion:
Variance of X< Variance of Y