Statistics
Mean and variance with two unknowns
nta_pyq_2025_apr
Grade 12
Question:
If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then$a + b + ab$is equal to :
Step-by-Step Solution
Key Concept: Translate the given mean and variance with two unknowns into equations using$$\bar{x}$=$\tfrac{\sum x_i}${n}$and the variance formula.
∵$mean = 9$∴$53 + a + b = 72$(2) $\Rightarrow$$a + b = 19$2 37$\sumx$2 ¯ ¯¯¯ 2 2 1 ∵ $\sigma$ = and (X) + $\sigma$ = 4 N 2 2 37$529 + a + b$$\Rightarrow$ 81 + = 4 8 2 2 $\Rightarrow$$648 + 74 = 529 + a + b$2 2 $\Rightarrow$$a + b = 193$2 2 ∵$a + b = 19$$\Rightarrow$$a + b + 2ab = 361$$\Rightarrow$$2ab = 168$$\Rightarrow$$ab = 84$∴$a + b + ab = 103$
Correct Answer: 2