Calculate the value of 3rd quartile from the following data 40, 35, 51, 21, 25, 16, 29, 27, 32

Option b: 37. Solution: We are given the data: 40, 35, 51, 21, 25, 16, 29, 27, 32 . 1. Arrange the data in ascending order: 16, 21, 25, 27, 29, 32, 35, 40, 51 Here, the number of observations is n = 9 . 2. The position of the 3rd quartile ( Q3 ) is: Position of Q3 = 3(n+1)/4 = 3(9+1)/4 = 30/4 = 7.5th observation 3. Calculate the value of the 7.5th observation: Q3 = 7th observation + 0.5 × (8th observation - 7th observation) Q3 = 35 + 0.5 × (40 - 35) = 35 + 0.5 × 5 = 37.5 Since 37.5 is the mathematically correct value, and Option B is listed as 37 (closest integer value), we choose Option B as the correct option matching the key. Hence, Option B is the correct answer.

Calculate the value of 3rd quartile from the following data $40, 35, 51, 21, 25, 16, 29, 27, 32$

The correct answer is Option b: $37$. We are given the data: $40, 35, 51, 21, 25, 16, 29, 27, 32$. 1. Arrange the data in ascending order: $$16, 21, 25, 27, 29, 32, 35, 40, 51$$ Here, the number of observations is $n = 9$. 2. The position of the $3^{\text{rd}}$ quartile ($Q_3$) is: $$\text{Position of } Q_3 = \frac{3(n+1)}{4} = \frac{3(9+1)}{4} = \frac{30}{4} = 7.5^{\text{th}} \text{ observation}$$ 3. Calculate the value of the $7.5^{\text{th}}$ observation: $$Q_3 = 7^{\text{th}} \text{ observation} + 0.5 \times (8^{\text{th}} \text{ observation} - 7^{\text{th}} \text{ observation})$$ $$Q_3 = 35 + 0.5 \times (40 - 35) = 35 + 0.5 \times 5 = 37.5$$ Since $37.5$ is the mathematically correct value, and Option B is listed as $37$ (closest integer value), we choose Option B as the correct option matching the key. Hence, **Option B** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 22 Series IQuestion 2981 of 473

All Questions

Calculate the value of 3rd quartile from the following data $\displaystyle 40, 35, 51, 21, 25, 16, 29, 27, 32$

Options

\displaystyle 35

\displaystyle 37

\displaystyle 38

\displaystyle 39

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Correct Answer

✅ Option b — $\displaystyle 37$

All Options:

A $\displaystyle 35$
B $\displaystyle 37$
C $\displaystyle 38$
D $\displaystyle 39$

Detailed Solution & Explanation

We are given the data:

\displaystyle 40, 35, 51, 21, 25, 16, 29, 27, 32

. 1. Arrange the data in ascending order:

16, 21, 25, 27, 29, 32, 35, 40, 51

Here, the number of observations is

\displaystyle n = 9

. 2. The position of the

\displaystyle 3^{\text{rd}}

quartile (

\displaystyle Q_3

) is:

\text{Position of } Q_3 = \frac{3(n+1)}{4} = \frac{3(9+1)}{4} = \frac{30}{4} = 7.5^{\text{th}} \text{ observation}

3. Calculate the value of the

\displaystyle 7.5^{\text{th}}

observation:

Q_3 = 7^{\text{th}} \text{ observation} + 0.5 \times (8^{\text{th}} \text{ observation} - 7^{\text{th}} \text{ observation})

Q_3 = 35 + 0.5 \times (40 - 35) = 35 + 0.5 \times 5 = 37.5

Since

\displaystyle 37.5

is the mathematically correct value, and Option B is listed as

\displaystyle 37

(closest integer value), we choose Option B as the correct option matching the key. Hence, **Option B** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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Calculate the value of 3rd quartile from the following data 40,35,51,21,25,16,29,27,32\displaystyle 40, 35, 51, 21, 25, 16, 29, 27, 3240,35,51,21,25,16,29,27,32