If the mean and the variance of the data

Class

4–8

8–12

12–16

16–20

Frequency

3

$λ$

4

7

are $μ and 19$ respectively, then the value of $λ + μ$ is. [2026]

Question

If the mean and the variance of the data

Class	4–8	8–12	12–16	16–20
Frequency	3	$λ$	4	7

are $μ and 19$ respectively, then the value of $λ + μ$ is. [2026]

Smart Achievers · Accepted Answer

(4)

$μ = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{18 + 10 λ + 56 + 126}{14 + λ}$

$= \frac{200 + 10 λ}{λ + 14} = 10 + (\frac{60}{λ + 14})$

$λ + 14 is a multiple of 60 \Rightarrow λ = 1, 6 or 16$

$σ^{2} = \frac{\sum f_{i} x_{i}^{2}}{λ + 14} - μ^{2}$

$σ^{2} = \frac{6^{2} (3) + 10^{2} (λ) + 14^{2} (4) + 18^{2} (7)}{λ + 14} - μ^{2}$

$for λ = 6, μ = 10 + 3 = 13$

$λ + μ = 19$

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