The mean deviation of the numbers 3, 10, 6, 11, 14, 17, 9, 8, 12 about the mean is:

Option c: 3.1. Solution: We are given the dataset: 3, 10, 6, 11, 14, 17, 9, 8, 12 . The number of observations is n = 9 . 1. Calculate the arithmetic mean ( x ): x = 3 + 10 + 6 + 11 + 14 + 17 + 9 + 8 + 12/9 = 90/9 = 10 2. Calculate absolute deviations from the mean |xi - x| : - |3 - 10| = 7 - |10 - 10| = 0 - |6 - 10| = 4 - |11 - 10| = 1 - |14 - 10| = 4 - |17 - 10| = 7 - |9 - 10| = 1 - |8 - 10| = 2 - |12 - 10| = 2 3. Calculate the sum of absolute deviations: sum |xi - x| = 7 + 0 + 4 + 1 + 4 + 7 + 1 + 2 + 2 = 28 4. Calculate Mean Deviation: M.D. = 28/9 ≈ 3.11 Hence, Option C is the correct answer.

The mean deviation of the numbers $3, 10, 6, 11, 14, 17, 9, 8, 12$ about the mean is:

The correct answer is Option c: 3.1. We are given the dataset: $3, 10, 6, 11, 14, 17, 9, 8, 12$. The number of observations is $n = 9$. 1. Calculate the arithmetic mean ($\bar{x}$): $$\bar{x} = \frac{3 + 10 + 6 + 11 + 14 + 17 + 9 + 8 + 12}{9} = \frac{90}{9} = 10$$ 2. Calculate absolute deviations from the mean $|x_i - \bar{x}|$: - $|3 - 10| = 7$ - $|10 - 10| = 0$ - $|6 - 10| = 4$ - $|11 - 10| = 1$ - $|14 - 10| = 4$ - $|17 - 10| = 7$ - $|9 - 10| = 1$ - $|8 - 10| = 2$ - $|12 - 10| = 2$ 3. Calculate the sum of absolute deviations: $$\sum |x_i - \bar{x}| = 7 + 0 + 4 + 1 + 4 + 7 + 1 + 2 + 2 = 28$$ 4. Calculate Mean Deviation: $$\text{M.D.} = \frac{28}{9} \approx 3.11$$ Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQPYQ July 21Question 3096 of 473

All Questions

The mean deviation of the numbers $\displaystyle 3, 10, 6, 11, 14, 17, 9, 8, 12$ about the mean is:

Options

A8.7

B4.2

C3.1

D9.8

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

Correct Answer

✅ Option c — 3.1

All Options:

A8.7
B4.2
C3.1
D9.8

Detailed Solution & Explanation

We are given the dataset:

\displaystyle 3, 10, 6, 11, 14, 17, 9, 8, 12

. The number of observations is

\displaystyle n = 9

. 1. Calculate the arithmetic mean (

\displaystyle \bar{x}

\bar{x} = \frac{3 + 10 + 6 + 11 + 14 + 17 + 9 + 8 + 12}{9} = \frac{90}{9} = 10

2. Calculate absolute deviations from the mean

\displaystyle |x_i - \bar{x}|

: -

\displaystyle |3 - 10| = 7

\displaystyle |10 - 10| = 0

\displaystyle |6 - 10| = 4

\displaystyle |11 - 10| = 1

\displaystyle |14 - 10| = 4

\displaystyle |17 - 10| = 7

\displaystyle |9 - 10| = 1

\displaystyle |8 - 10| = 2

\displaystyle |12 - 10| = 2

3. Calculate the sum of absolute deviations:

\sum |x_i - \bar{x}| = 7 + 0 + 4 + 1 + 4 + 7 + 1 + 2 + 2 = 28

4. Calculate Mean Deviation:

\text{M.D.} = \frac{28}{9} \approx 3.11

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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The mean deviation of the numbers 3,10,6,11,14,17,9,8,12\displaystyle 3, 10, 6, 11, 14, 17, 9, 8, 123,10,6,11,14,17,9,8,12 about the mean is: