Question
Mathematics Question on Measures of Dispersion
The mean square deviation of a set of n observation x1,x2,...xn about a point c is defined as n1i=1∑n(xi−c)2.The mean square deviations about −2 and 2 are 18 and 10 respectively, the standard deviation of this set of observations is
A
3
B
2
C
1
D
None of these
Answer
3
Explanation
Solution
We have n1i=1∑n(xi+2)2=18 and
n1i=1∑n(xi−2)2=10
⇒i=1∑n(xi+2)2=18n and
i=1∑n(xi−2)2=10n
⇒i=1∑n(xi+2)2+i=1∑n(xi−2)2=28n
and i=1∑n(xi+2)2−i=1∑n(xi−2)2=8n
⇒2i=1∑n(xi+4)2=28n2i=1∑n4xi=8n
⇒i=1∑nxi2+4n=14ni=1∑nxi=n
⇒i=1∑nxi2=10ni=1∑nxi=n
∴σ=n1i=1∑nxi2−(n1i=1∑nxi)2
=n10n−(nn)2=3