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Best Suited Measure of Central Tendency in Different Cases and the Empirical Relationship between Them

Assertion :If...

Question

Assertion :If mean & median of an asymmetrical distribution are $58$ & $61$ respectively, then Mode $= 67$ . Reason: For an asymmetrical distribution Mode $= 3$ Median $- 2$ Mean .

Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.

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Both Assertion & Reason are individually true but Reason is not the correct (proper) explanation of Assertion.

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Assertion is true Reason is false.

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Assertion is false Reason is true.

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Solution

The correct option is A Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.
$∵$ Mode $= 3$ Median $- 2$ Mean

given, Mean $= 58$ & Median $= 61$

Thus,

$Mode = 3 \times 61 - 2 \times 58 = 67$

Hence Assertion & Reason bth are correct and Reason is correct explanation of Assertion.

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Similar questions

Q. Assertion (A)
If the median and mode of a frequency distribution are 150 and 154 respectively, then its mean is 148.
Reason (R)
Mean, median and mode of a frequency distribution are related as:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is a not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion: The mean of 15 numbers is 25. If 6 is subtracted from each number, the mean of new numbers is 19.
Reason: Mode = 3(median) − 2(mean).
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true and Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Assertion-and-Reason Type

Each question consists of two statements,namely,Assertion (A) and Reason (R).For selecting the correct answer,use the following code:

(a) Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A).

(d) Assertion (A) is false and Reason (R) is true.

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) I f t h e m e d i a n a n d m o d e o f a & M e a n, m e d i a n a n d m o d e o f a f r e q u e n c y d i s t r i b u t i o n a r e 150 a n d & f r e q u e n c y d i s t r i b u t i o n a r e r e l a t e d a s : 154 r e s p e c t i v e l y, t h e n i t s m e a n i s 148. & m o d e = 3 m e d i a n - 2 m e a n . \end{matrix}$

The correct answer is :(a)/(b)/(c)/(d).

Q. Assertion: Median of 51, 70, 65, 82, 60, 68, 62, 95, 55, 64, 58, 75, 80, 85, 90 is 68.
Reason: When n observations are arranged in an ascending order and n is odd, then

median = value of \frac{1}{2} (n + 1)

th observation.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true and Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q. Read the assertion and reason carefully to mark the correct option out of the options given below:
(a)If both assertion and reason are true and the reason is the correct explanation of the assertion
(b)If both assertion and reason are true but reason is not the correct explanation of the assertion
(c)If assertion is true but reason is false.
(d)If assertion and reason both are false.
Assertion: Salvarsan is an antidepressant drug.
Reason: It is a derivative of barbituric acid.

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Assertion :If mean & median of an asymmetrical distribution are 58 & 61respectively, then Mode =67. Reason: For an asymmetrical distribution Mode =3 Median −2 Mean .

The correct option is A Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.∵ Mode =3 Median −2 Meangiven, Mean=58 & Median=61Thus, Mode=3×61−2×58=67Hence Assertion & Reason bth are correct and Reason is correct explanation of Assertion.

Assertion :If mean & median of an asymmetrical distribution are $58$ & $61$ respectively, then Mode $= 67$ . Reason: For an asymmetrical distribution Mode $= 3$ Median $- 2$ Mean .