The QD of six numbers 13, 8, 36, 40, 38, 41 is equal to:

Option c: 13.5. Solution: We are given the observations: 13, 8, 36, 40, 38, 41. 1. Arrange the data in ascending order: 8, 13, 36, 38, 40, 41 Here, the number of observations is n = 6. 2. Find the first quartile (Q1) and third quartile (Q3) using the simplified method for small datasets: - Q1 = 13 (the second value). - Q3 = 40 (the fifth value). 3. Calculate the Quartile Deviation (Q.D.): text{Q.D.} = Q3 - Q1/2 = 40 - 13/2 = 27/2 = 13.5 Hence, Option C is the correct answer.

The QD of six numbers $13, 8, 36, 40, 38, 41$ is equal to:

The correct answer is Option c: $13.5$. We are given the observations: $13, 8, 36, 40, 38, 41$. 1. Arrange the data in ascending order: $$8, 13, 36, 38, 40, 41$$ Here, the number of observations is $n = 6$. 2. Find the first quartile ($Q_1$) and third quartile ($Q_3$) using the simplified method for small datasets: - $Q_1 = 13$ (the second value). - $Q_3 = 40$ (the fifth value). 3. Calculate the Quartile Deviation (Q.D.): $$\text{Q.D.} = \frac{Q_3 - Q_1}{2} = \frac{40 - 13}{2} = \frac{27}{2} = 13.5$$ Hence, **Option C** is the correct answer.

Central Tendency & DispersionMTP Dec 22 Series IIQuestion 3247 of 473

All Questions

The QD of six numbers $\displaystyle 13, 8, 36, 40, 38, 41$ is equal to:

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 13, 8, 36, 40, 38, 41

. 1. Arrange the data in ascending order:

8, 13, 36, 38, 40, 41

Here, the number of observations is

\displaystyle n = 6

. 2. Find the first quartile (

\displaystyle Q_1

) and third quartile (

\displaystyle Q_3

) using the simplified method for small datasets: -

\displaystyle Q_1 = 13

(the second value). -

\displaystyle Q_3 = 40

(the fifth value). 3. Calculate the Quartile Deviation (Q.D.):

\text{Q.D.} = \frac{Q_3 - Q_1}{2} = \frac{40 - 13}{2} = \frac{27}{2} = 13.5

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

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The QD of six numbers 13,8,36,40,38,41\displaystyle 13, 8, 36, 40, 38, 4113,8,36,40,38,41 is equal to: