What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16 ?

Option c: 12.75. Solution: To find the first quartile ( Q1 ) for the observations: 15, 18, 10, 20, 23, 28, 12, 16 : 1. Arrange the data in ascending order: 10, 12, 15, 16, 18, 20, 23, 28 Here, the number of observations is n = 8 . 2. The position of Q1 is given by: Position of Q1 = n+1/4 = 8+1/4 = 2.25th observation 3. Calculate the value of the 2.25th observation: Q1 = 2nd observation + 0.25 × (3rd observation - 2nd observation) Q1 = 12 + 0.25 × (15 - 12) = 12 + 0.25 × 3 = 12.75 Hence, Option C is the correct answer.

Measures of Central Tendency and DispersionMCQMTP May 19Question 2970 of 473

All Questions

What is the value of the first quartile for observations $\displaystyle 15, 18, 10, 20, 23, 28, 12, 16$ ?

Options

\displaystyle 17

\displaystyle 16

\displaystyle 12.75

\displaystyle 12

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Correct Answer

✅ Option c — $\displaystyle 12.75$

All Options:

A $\displaystyle 17$
B $\displaystyle 16$
C $\displaystyle 12.75$
D $\displaystyle 12$

Detailed Solution & Explanation

To find the first quartile (

\displaystyle Q_1

) for the observations:

\displaystyle 15, 18, 10, 20, 23, 28, 12, 16

: 1. Arrange the data in ascending order:

10, 12, 15, 16, 18, 20, 23, 28

Here, the number of observations is

\displaystyle n = 8

. 2. The position of

\displaystyle Q_1

is given by:

\text{Position of } Q_1 = \frac{n+1}{4} = \frac{8+1}{4} = 2.25^{\text{th}} \text{ observation}

3. Calculate the value of the

\displaystyle 2.25^{\text{th}}

observation:

Q_1 = 2^{\text{nd}} \text{ observation} + 0.25 \times (3^{\text{rd}} \text{ observation} - 2^{\text{nd}} \text{ observation})

Q_1 = 12 + 0.25 \times (15 - 12) = 12 + 0.25 \times 3 = 12.75

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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What is the value of the first quartile for observations 15,18,10,20,23,28,12,16\displaystyle 15, 18, 10, 20, 23, 28, 12, 1615,18,10,20,23,28,12,16?