Find Q1 for the following observations: 7,9,5,4,10,15,14,18,6,20

Option c: 5.75. Solution: To find the first quartile ( Q1 ) for the observations: 7, 9, 5, 4, 10, 15, 14, 18, 6, 20 : 1. Arrange the data in ascending order: 4, 5, 6, 7, 9, 10, 14, 15, 18, 20 Here, the number of observations is n = 10 . 2. The position of Q1 is given by: Position of Q1 = n+1/4 = 10+1/4 = 2.75th observation 3. Calculate the value of the 2.75th observation: Q1 = 2nd observation + 0.75 × (3rd observation - 2nd observation) Q1 = 5 + 0.75 × (6 - 5) = 5 + 0.75 × 1 = 5.75 Hence, Option C is the correct answer.

Measures of Central Tendency and DispersionMCQMTP June 24 Series IIQuestion 2988 of 473

All Questions

Find $\displaystyle Q_1$ for the following observations: $\displaystyle 7,9,5,4,10,15,14,18,6,20$

Options

\displaystyle 4.75

\displaystyle 5.25

\displaystyle 5.75

\displaystyle 6.25

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Correct Answer

✅ Option c — $\displaystyle 5.75$

All Options:

A $\displaystyle 4.75$
B $\displaystyle 5.25$
C $\displaystyle 5.75$
D $\displaystyle 6.25$

Detailed Solution & Explanation

To find the first quartile (

\displaystyle Q_1

) for the observations:

\displaystyle 7, 9, 5, 4, 10, 15, 14, 18, 6, 20

: 1. Arrange the data in ascending order:

4, 5, 6, 7, 9, 10, 14, 15, 18, 20

Here, the number of observations is

\displaystyle n = 10

. 2. The position of

\displaystyle Q_1

is given by:

\text{Position of } Q_1 = \frac{n+1}{4} = \frac{10+1}{4} = 2.75^{\text{th}} \text{ observation}

3. Calculate the value of the

\displaystyle 2.75^{\text{th}}

observation:

Q_1 = 2^{\text{nd}} \text{ observation} + 0.75 \times (3^{\text{rd}} \text{ observation} - 2^{\text{nd}} \text{ observation})

Q_1 = 5 + 0.75 \times (6 - 5) = 5 + 0.75 \times 1 = 5.75

Hence, **Option C** 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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Find Q1\displaystyle Q_1Q1​ for the following observations: 7,9,5,4,10,15,14,18,6,20\displaystyle 7,9,5,4,10,15,14,18,6,207,9,5,4,10,15,14,18,6,20