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JEE Main 2022 · 26 Jun · Shift 2, Mathematics question 17

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :

Choose one option
Answer and worked solution

Official answer: C

Find the observations. Wrong total 750, correct total 800, so correct − wrong =50=50; with sum 70, correct =60=60, wrong =10=10.

Sum of squares. Wrong: 50(4+225)=1145050(4+225)=11450; correct: 11450−100+3600=1495011450-100+3600=14950.

Variance. 1495050−162=299−256=43\frac{14950}{50}-16^2=299-256=43.

(C)

Topics:Variance and standard deviationMeasures of central tendency
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