Find D6 for the following observations. 7, 9, 5, 4, 10, 15, 14, 18, 6, 20

Option b: 12.40. Solution: To find the 6th decile ( D6 ) 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 D6 is given by: Position of D6 = 6(n+1)/10 = 6(10+1)/10 = 66/10 = 6.6th term 3. Calculate the value of the 6.6th term: D6 = 6th term + 0.6 × (7th term - 6th term) D6 = 10 + 0.6 × (14 - 10) = 10 + 0.6 × 4 = 10 + 2.4 = 12.4 Since 12.40 is the mathematically correct value, and Option B is closest or represents the correct choice (noting textbook key discrepancies that may list Option B), we select Option B. Hence, Option B is the correct answer.

Find $D_6$ for the following observations. $7, 9, 5, 4, 10, 15, 14, 18, 6, 20$

The correct answer is Option b: $12.40$. To find the $6^{\text{th}}$ decile ($D_6$) 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 $D_6$ is given by: $$\text{Position of } D_6 = \frac{6(n+1)}{10} = \frac{6(10+1)}{10} = \frac{66}{10} = 6.6^{\text{th}} \text{ term}$$ 3. Calculate the value of the $6.6^{\text{th}}$ term: $$D_6 = 6^{\text{th}} \text{ term} + 0.6 \times (7^{\text{th}} \text{ term} - 6^{\text{th}} \text{ term})$$ $$D_6 = 10 + 0.6 \times (14 - 10) = 10 + 0.6 \times 4 = 10 + 2.4 = 12.4$$ Since $12.40$ is the mathematically correct value, and Option B is closest or represents the correct choice (noting textbook key discrepancies that may list Option B), we select Option B. Hence, **Option B** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Nov 21Question 2977 of 473

All Questions

Find $\displaystyle D_6$ for the following observations. $\displaystyle 7, 9, 5, 4, 10, 15, 14, 18, 6, 20$

Options

\displaystyle 11.40

\displaystyle 12.40

\displaystyle 13.40

\displaystyle 13.80

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — $\displaystyle 12.40$

All Options:

A $\displaystyle 11.40$
B $\displaystyle 12.40$
C $\displaystyle 13.40$
D $\displaystyle 13.80$

Detailed Solution & Explanation

To find the

\displaystyle 6^{\text{th}}

decile (

\displaystyle D_6

) 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 D_6

is given by:

\text{Position of } D_6 = \frac{6(n+1)}{10} = \frac{6(10+1)}{10} = \frac{66}{10} = 6.6^{\text{th}} \text{ term}

3. Calculate the value of the

\displaystyle 6.6^{\text{th}}

term:

D_6 = 6^{\text{th}} \text{ term} + 0.6 \times (7^{\text{th}} \text{ term} - 6^{\text{th}} \text{ term})

D_6 = 10 + 0.6 \times (14 - 10) = 10 + 0.6 \times 4 = 10 + 2.4 = 12.4

Since

\displaystyle 12.40

is the mathematically correct value, and Option B is closest or represents the correct choice (noting textbook key discrepancies that may list Option B), we select Option B. 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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Find D6\displaystyle D_6D6​ 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