The Q.D of 6 numbers 15, 8, 36, 40, 38, 41 is

Option c: 13.5. Solution: We are given the observations: 15, 8, 36, 40, 38, 41. 1. Arrange the data in ascending order: 8, 15, 36, 38, 40, 41 Here, the number of observations is n = 6. 2. Find the first quartile (Q1): - Position of Q1 = 6+1/4 = 1.75^{text{th}} term. - Q1 = 8 + 0.75 x (15 - 8) = 13.25. 3. Find the third quartile (Q3): - Position of Q3 = 3(6+1)/4 = 5.25^{text{th}} term. - Q3 = 40 + 0.25 x (41 - 40) = 40.25. 4. Calculate Quartile Deviation (Q.D.): text{Q.D.} = Q3 - Q1/2 = 40.25 - 13.25/2 = 27/2 = 13.5 Hence, Option C is the correct answer.

The Q.D of $6$ numbers $15, 8, 36, 40, 38, 41$ is

The correct answer is Option c: $13.5$. We are given the observations: $15, 8, 36, 40, 38, 41$. 1. Arrange the data in ascending order: $$8, 15, 36, 38, 40, 41$$ Here, the number of observations is $n = 6$. 2. Find the first quartile ($Q_1$): - Position of $Q_1 = \frac{6+1}{4} = 1.75^{\text{th}}$ term. - $Q_1 = 8 + 0.75 \times (15 - 8) = 13.25$. 3. Find the third quartile ($Q_3$): - Position of $Q_3 = \frac{3(6+1)}{4} = 5.25^{\text{th}}$ term. - $Q_3 = 40 + 0.25 \times (41 - 40) = 40.25$. 4. Calculate Quartile Deviation (Q.D.): $$\text{Q.D.} = \frac{Q_3 - Q_1}{2} = \frac{40.25 - 13.25}{2} = \frac{27}{2} = 13.5$$ Hence, **Option C** is the correct answer.

Central Tendency & DispersionPYQ June 19Question 3217 of 473

All Questions

The Q.D of $\displaystyle 6$ numbers $\displaystyle 15, 8, 36, 40, 38, 41$ is

Options

\displaystyle 12.5

\displaystyle 25

\displaystyle 13.5

\displaystyle 37

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Correct Answer

✅ Option c — $\displaystyle 13.5$

All Options:

A $\displaystyle 12.5$
B $\displaystyle 25$
C $\displaystyle 13.5$
D $\displaystyle 37$

Detailed Solution & Explanation

We are given the observations:

\displaystyle 15, 8, 36, 40, 38, 41

. 1. Arrange the data in ascending order:

8, 15, 36, 38, 40, 41

Here, the number of observations is

\displaystyle n = 6

. 2. Find the first quartile (

\displaystyle Q_1

): - Position of

\displaystyle Q_1 = \frac{6+1}{4} = 1.75^{\text{th}}

term. -

\displaystyle Q_1 = 8 + 0.75 \times (15 - 8) = 13.25

. 3. Find the third quartile (

\displaystyle Q_3

): - Position of

\displaystyle Q_3 = \frac{3(6+1)}{4} = 5.25^{\text{th}}

term. -

\displaystyle Q_3 = 40 + 0.25 \times (41 - 40) = 40.25

. 4. Calculate Quartile Deviation (Q.D.):

\text{Q.D.} = \frac{Q_3 - Q_1}{2} = \frac{40.25 - 13.25}{2} = \frac{27}{2} = 13.5

Hence, **Option C** is the correct answer.

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The Q.D of 6\displaystyle 66 numbers 15,8,36,40,38,41\displaystyle 15, 8, 36, 40, 38, 4115,8,36,40,38,41 is