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

Assertion-and...

Question

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).

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

(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).

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Solution

Mode = 3 $\times$ Median - 2 $\times$ Mean

from A

$M e a n = \frac{3 \times M e d i a n - m o d e}{2} = \frac{3 \times 150 - 154}{2} = \frac{450 - 154}{2} = \frac{296}{2} = 148$

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

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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.

This 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 true and Reason (R) correct explanation of Assertion (A).

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

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

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) If ABCD is a rhombus whose one & Median of a triangle divides it angle is 60^{\circ} then the ratio of the & into two triangles of equal area. lenghts of its diagonals is \sqrt{3} : 1. \end{matrix}$

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

This 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 true and Reason (R) correct explanation of Assertion (A).

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

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) The area of a trapezium whose & The area of an equailateral traingle parallel sides measure 25 cm and & of side 8 cm is 16 \sqrt{3} c m^{2} . 15 cm respectively and the distance between them is 6 cm,is 120 c m^{2} . \end{matrix}$

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

This 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 true and Reason (R) correct explanation of Assertion (A).

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

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) The diagonals of a | | g m d i v i d e i t & A diagonal of a | | g m d i v i d e s i t i n t o into four triangles of equal area. & two diagonals of equal area. \end{matrix}$

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

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

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

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

$\begin{matrix} A s s e r t i o n (A) & R e a s o n (R) T h e c u r v e d s u r f a c e a r e a o f a & V o l u m e o f a c o n e = π r^{2} h . c o n e o f b a s e r a d i u s 3 c m a n d h e i g h t 4 c m i s (15 π) c m^{2} . \end{matrix}$

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

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Mode = 3 ×Median - 2×Mean from A Mean=3×Median−mode2=3×150−1542=450−1542=2962=148 So (a) Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).

Mode = 3 $\times$ Median - 2 $\times$ Mean

from A

$M e a n = \frac{3 \times M e d i a n - m o d e}{2} = \frac{3 \times 150 - 154}{2} = \frac{450 - 154}{2} = \frac{296}{2} = 148$

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