NIMCET 2014 Mathematics PYQ — In a group of 200 students, the mean and the standard deviation o… | Mathem Solvex | Mathem Solvex
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NIMCET 2014 — Mathematics PYQ
NIMCET | Mathematics | 2014
In a group of 200 students, the mean and the standard deviation of scores were found to be 40 and 15, respectively. Later on, it was found that the two scores 43 and 35 were misread as 34 and 53, respectively. The corrected mean of scores is:
Choose the correct answer:
A.
40.965
B.
39.035
C.
39.965
(Correct Answer)
D.
40.035
Correct Answer:
39.965
Explanation
Concept
Average/Mean:Mean of ’n’ observations=xˉ=nSum of Observations
If some values are changed/added/removed, then:
Averagenew=Averageold+(Average of the change)
Solution
Step 1: Identify the given data
Total number of students (n) = 200
Old Mean (xˉold) = 40
Correct scores: 43 and 35
Incorrect scores (misread as): 34 and 53
Step 2: Calculate the net change in the sum
Change in value=(Correct scores)−(Incorrect scores)
Change=(43−34)+(35−53)
Change=9+(−18)=−7
Step 3: Calculate the corrected mean
Using the formula Averagenew=Averageold+(nNet Change):
Averagenew=40+(200−7)
Averagenew=40−0.035
Averagenew=39.965
Correct Option: 3
Explanation
Concept
Average/Mean:Mean of ’n’ observations=xˉ=nSum of Observations
If some values are changed/added/removed, then:
Averagenew=Averageold+(Average of the change)
Solution
Step 1: Identify the given data
Total number of students (n) = 200
Old Mean (xˉold) = 40
Correct scores: 43 and 35
Incorrect scores (misread as): 34 and 53
Step 2: Calculate the net change in the sum
Change in value=(Correct scores)−(Incorrect scores)
Change=(43−34)+(35−53)
Change=9+(−18)=−7
Step 3: Calculate the corrected mean
Using the formula Averagenew=Averageold+(nNet Change):
