CUET PG 2022 Mathematics PYQ — The arithmetic mean and standard deviation of series of 20 items … | Mathem Solvex | Mathem Solvex
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CUET PG 2022 — Mathematics PYQ
CUET PG | Mathematics | 2022
The arithmetic mean and standard deviation of series of 20 items were calculated by a student as 20 cm and 5 cm respectively. But while calculating them an item 15 was misread as 30. Find the correct standard deviation.
Choose the correct answer:
A.
4.10
B.
4.40
C.
4.54
(Correct Answer)
D.
4.66
Correct Answer:
4.54
Explanation
The correct mean is:
xˉcorrect=n∑xcorrect=20385=19.25 cm
The correct variance (σcorrect2) is:
σcorrect2=n∑xcorrect2−(xˉcorrect)2
σcorrect2=207825−(19.25)2
σcorrect2=391.25−370.5625=20.6875
The correct standard deviation is the square root of the correct variance:
σcorrect=σcorrect2=20.6875≈4.55 cm
Explanation
The correct mean is:
xˉcorrect=n∑xcorrect=20385=19.25 cm
The correct variance (σcorrect2) is:
σcorrect2=n∑xcorrect2−(xˉcorrect)2
σcorrect2=207825−(19.25)2
σcorrect2=391.25−370.5625=20.6875
The correct standard deviation is the square root of the correct variance:
