The third decile for the numbers 15, 10, 20, 25, 18, 11, 9, 12 is

Option b: 10.70. Solution: To find the 3rd decile ( D3 ) for the observations: 15, 10, 20, 25, 18, 11, 9, 12 : 1. Arrange the data in ascending order: 9, 10, 11, 12, 15, 18, 20, 25 Here, the number of observations is n = 8 . 2. The position of D3 is given by: Position of D3 = 3(n+1)/10 = 3(8+1)/10 = 27/10 = 2.7th term 3. Calculate the value of the 2.7th term: D3 = 2nd term + 0.7 × (3rd term - 2nd term) D3 = 10 + 0.7 × (11 - 10) = 10 + 0.7 × 1 = 10.70 Hence, Option B is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Nov 19Question 2971 of 473

All Questions

The third decile for the numbers $\displaystyle 15, 10, 20, 25, 18, 11, 9, 12$ is

Options

\displaystyle 13

\displaystyle 10.70

\displaystyle 11

\displaystyle 11.50

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Correct Answer

✅ Option b — $\displaystyle 10.70$

All Options:

A $\displaystyle 13$
B $\displaystyle 10.70$
C $\displaystyle 11$
D $\displaystyle 11.50$

Detailed Solution & Explanation

To find the

\displaystyle 3^{\text{rd}}

decile (

\displaystyle D_3

) for the observations:

\displaystyle 15, 10, 20, 25, 18, 11, 9, 12

: 1. Arrange the data in ascending order:

9, 10, 11, 12, 15, 18, 20, 25

Here, the number of observations is

\displaystyle n = 8

. 2. The position of

\displaystyle D_3

is given by:

\text{Position of } D_3 = \frac{3(n+1)}{10} = \frac{3(8+1)}{10} = \frac{27}{10} = 2.7^{\text{th}} \text{ term}

3. Calculate the value of the

\displaystyle 2.7^{\text{th}}

term:

D_3 = 2^{\text{nd}} \text{ term} + 0.7 \times (3^{\text{rd}} \text{ term} - 2^{\text{nd}} \text{ term})

D_3 = 10 + 0.7 \times (11 - 10) = 10 + 0.7 \times 1 = 10.70

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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The third decile for the numbers 15,10,20,25,18,11,9,12\displaystyle 15, 10, 20, 25, 18, 11, 9, 1215,10,20,25,18,11,9,12 is