Consider the following frequency distribution : Value 4 5 8 9 6 12 11 Frequency 5 f 1 f 2 2 1 1 3 Suppose that the sum of the frequencies is 19 and the median of this frequency distribution is 6.

Question

Consider the following frequency distribution :

Value	4	5	8	9	6	12	11
Frequency	5	$f_{1}$	$f_{2}$	2	1	1	3

Suppose that the sum of the frequencies is 19 and the median of this frequency distribution is 6. For the given frequency distribution, let $α$ denote the mean deviation about the mean, $β$ denote the mean deviation about the median, and $σ^{2}$ denote the variance. Match each entry in List-I to the correct entry in List-II and choose the correct option. $(P) (Q) (R) (S) LIST - I 7 f_{1} + 9 f_{2} is equal to 19 α is equal to 19 β is equal to 19 σ^{2} is equal to (1) (2) (3) (4) (5) LIST - II 146474814555$

Options:

Answer:

C

Solution:

$X_{i} 456891112 f_{i} 5413231 \overset{x}{ˉ} = 7 d_{i} = ∣ x_{i} - \overset{x}{ˉ} ∣ 3211245 M = 6 ei = ∣ xi - M ∣ 2102356 \sum f_{i} d_{i} 15813412548 \sum f_{i} e_{i} 10406615647 Σ f_{i} d_{i}^{2} 45161384825146$
$f_{1} = 4 f_{2} = 3 α = \frac{48}{19}, β = \frac{47}{19}, σ^{2} = \frac{146}{19}$

TestHub · Accepted Answer

X i ​ 4 5 6 8 9 11 12 ​ f i ​ 5 4 1 3 2 3 1 ​ x ˉ = 7 d i ​ = ∣ x i ​ − x ˉ ∣ ​ 3 2 1 1 2 4 5 ​ M = 6 ei = ∣ xi − M ∣ ​ 2 1 0 2 3 5 6 ​ ∑ f i ​ d i ​ 15 8 1 3 4 12 5 48 ​ ∑ f i ​ e i ​ 10 4 0 6 6 15 6 47 ​ Σ f i ​ d i 2 ​ 45 16 1 3 8 48 25 146 ​ ​ ​ f 1 ​ = 4 f 2 ​ = 3 α = 19 48 ​ , β = 19 47 ​ , σ 2 = 19 146 ​ ​

Mathematics - Statistics Question with Solution | TestHub

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