If the variance of the frequency distribution x i 2 3 4 5 6 7 8 Frequency f i 3 6 16 α 9 5 6 is 3 , then α is equal to

We have, x i f i d i = x i - 5 f i d i 2 f i d i 2 3 - 3 27 - 9 3 6 - 2 24 - 12 4 16 - 1 16 - 16 5 α 0 0 0 6 9 1 9 9 7 5 2 20 10 8 6 3 54 18 σ x 2 = σ d 2 = ∑ f i d i 2 ∑ f i - ∑ f i d i ∑ f i 2 ⇒ 3 = 150 45 + α - 0 ⇒ 150 = 135 + 3 α ⇒ 3 α = 15 ⇒ α = 5

Mathematics - Statistics Question with Solution | TestHub

MathematicsStatisticsMeasures of DispersionEasy2 minPYQ_2023

MathematicsEasynumerical

If the variance of the frequency distribution

$x_{i}$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
Frequency $f_{i}$	$3$	$6$	$16$	$α$	$9$	$5$	$6$

is $3$ , then $α$ is equal to

Answer:

5.00

Solution:

We have,

$x_{i}$	$f_{i}$	$d_{i} = x_{i} - 5$	$f_{i} d_{i}^{2}$	$f_{i} d_{i}$
$2$	$3$	$- 3$	$27$	$- 9$
$3$	$6$	$- 2$	$24$	$- 12$
$4$	$16$	$- 1$	$16$	$- 16$
$5$	$α$	$0$	$0$	$0$
$6$	$9$	$1$	$9$	$9$
$7$	$5$	$2$	$20$	$10$
$8$	$6$	$3$	$54$	$18$

$σ_{x}^{2} = σ_{d}^{2} = \frac{\sum f_{i} d_{i}^{2}}{\sum f_{i}} - {(\frac{\sum f_{i} d_{i}}{\sum f_{i}})}^{2}$

$\Rightarrow 3 = \frac{150}{45 + α} - 0$

$\Rightarrow 150 = 135 + 3 α$

$\Rightarrow 3 α = 15 \Rightarrow α = 5$

Stream:JEESubject:MathematicsTopic:StatisticsSubtopic:Measures of Dispersion

⏱ 2mℹ️ Source: PYQ_2023

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