Statistics
Mean and variance of five observations
nta_pyq_2025_apr
Grade 12
Question:
Let the Mean and Variance of five observations$x = 1$,$x = 3$,$x = a$,$x = 7$and$x = b$,$a > b$, be 5 and 10 1 2 3 4 5 respectively. Then the Variance of the observations$n + x$,$n = 1$, 2,$\ldots$$\ldots$. .5 is n
Step-by-Step Solution
Key Concept: Translate the given mean and variance of five observations into equations using$$\bar{x}$=$\tfrac{\sum x_i}${n}$and the variance formula.
$\sum$xi$1 + 3 + a + 7 + b$x̄ = = = 5 (4) n 5$a + b = 14$2$\sumx$2 i 2 $\sigma$ = - (x̄) n 2 2 2 2 2$1 + 3 + a + 7 + b$$\Rightarrow$ -$25 = 10$5 2 2$a + b = 116$$a > b$$a = 10$$b = 4$n +$x_n$: 2, 5, 13, 11, 9 2 2 2 2 2 2$2 + 5 + 13 + 11 + 9$$2 + 5 + 13 + 11 + 9$2 $\sigma$ = - ( ) 5$5 = 80 - 64 = 16$option 4
Correct Answer: 4