NIMCET 2023 Mathematics PYQ — For a group of 100 candidates, the mean and standard deviation of… | Mathem Solvex | Mathem Solvex
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NIMCET 2023 — Mathematics PYQ
NIMCET | Mathematics | 2023
For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15 respectively. Later on, it was found that the scores 25 and 35 were misread as 52 and 53 respectively. Then the corrected mean and standard deviation corresponding to the corrected figures area
Choose the correct answer:
A.
39.9, 14.97
B.
39.5, 14
C.
39.55, 14.97
(Correct Answer)
D.
40.19, 15.1
Correct Answer:
39.55, 14.97
Explanation
1. Correcting the Mean:
n=100, xˉold=40
Sumold=100×40=4000
Correct Sum=4000−(52+53)+(25+35)
Correct Sum=4000−105+60=3955
xˉnew=1003955=39.55
2. Correcting the Sum of Squares (∑x2):
σold=15⟹σold2=225
σ2=n∑x2−(xˉ)2
225=100∑xold2−(40)2
225+1600=100∑xold2⟹∑xold2=182500
Now, subtract squares of wrong values and add squares of correct values:
∑xnew2=182500−(522+532)+(252+352)
∑xnew2=182500−(2704+2809)+(625+1225)
∑xnew2=182500−5513+1850=178837
3. Corrected Standard Deviation:
σnew2=100178837−(39.55)2
σnew2=1788.37−1564.2025=224.1675
σnew=224.1675≈14.9722
Correct Option: 3
Explanation
1. Correcting the Mean:
n=100, xˉold=40
Sumold=100×40=4000
Correct Sum=4000−(52+53)+(25+35)
Correct Sum=4000−105+60=3955
xˉnew=1003955=39.55
2. Correcting the Sum of Squares (∑x2):
σold=15⟹σold2=225
σ2=n∑x2−(xˉ)2
225=100∑xold2−(40)2
225+1600=100∑xold2⟹∑xold2=182500
Now, subtract squares of wrong values and add squares of correct values:
