The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken…
JEE Main 2021 — Mathematics Probability & Statistics
2021mcqmedium
The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35. If α and β are the mean and standard deviation respectively for correct data, then (α,β) is:
Official previous-year question
Held on 26 Aug 2021 · Verified 6 Jul 2026.
Options
A
(10.5,26)
B
(10.5,25)
C
(11,25)
D
(11,26)
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Solution
Mean =20x1+x2+x3+……+x19+25=10⇒x1+x2+x3+………+x19+25=200
⇒x1+x2+x3+………+x19=175
New mean =20x1+x2+x3+……+x19+35=20175+35=10.5
S.D. =20x12+x22+x32+……+x192+(25)2−(10)2
⇒2.5=20x12+x22+x32+……+x192+(25)2−(10)2
⇒x12+x22+x32+……+x192=1500
New S.D.=20x12+x22+x32+……+x192+(35)2−(10.5)2
=201500+(35)2−(110.25)
=26
(α,β)=(10.5,26)
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