NTA Abhyas JEE Main2020MathematicsStatisticsPractice

The mean and variance of 7 observations are 7 and 22 respectively. If 5 of the observations are 2,4 , 10 , 12,14 , then the remaining 2 observations are

Options

A4 , 3
B2 , 5
C6 , 1
D4 , 2

Correct answer

C. 6 , 1

Step-by-step solution

∴ Let x and y be remaining 2 observation Mean = 7 = 2 + 4 + 10 + 12 + 14 + x + y 7 ⇒ x + y = 7 ...(i) Variance = 22 = 1 7 2 2 + 4 2 + 10 2 + 12 2 + 14 2 + x 2 + y 2 - 7 2 ⇒ x 2 + y 2 = 37 ...(ii) Now solving (i) and (ii), we get, x = 1 , y = 6 or x = 6 , y = 1

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