Let the mean and variance of five observations x₁=1, x₂=3, x₃=a, x₄=7 and x₅=b, with a>b, be 5 and 10 respectively. Then the variance of the observations n + x n for n=1,2,,5 is:

Statistics and Probability: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q54

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumStatistics and Probability258× since 2002

Let the mean and variance of five observations

x_1=1

x_2=3

x_3=a

x_4=7

and

x_5=b

, with

a>b

, be

5

and

10

respectively. Then the variance of the observations

n + x_n

for

n=1,2,\dots,5

is: