The MD about the Mean for the data 6,9,11,10,12 is

Option c: 1.67. Solution: We are given the observations: 6, 9, 11, 10, 12 . The number of observations is n = 5 . 1. Calculate the arithmetic mean ( x ): x = 6 + 9 + 11 + 10 + 12/5 = 48/5 = 9.6 2. Calculate absolute deviations from the mean |xi - x| : - |6 - 9.6| = 3.6 - |9 - 9.6| = 0.6 - |11 - 9.6| = 1.4 - |10 - 9.6| = 0.4 - |12 - 9.6| = 2.4 3. Calculate sum of absolute deviations: sum |xi - x| = 3.6 + 0.6 + 1.4 + 0.4 + 2.4 = 8.4 4. Calculate Mean Deviation: M.D. = 8.4/5 = 1.68 Since 1.68 is the mathematically correct value, which is closest to 1.67 , we select Option C. Hence, Option C is the correct answer.

The MD about the Mean for the data $6,9,11,10,12$ is

The correct answer is Option c: $1.67$. We are given the observations: $6, 9, 11, 10, 12$. The number of observations is $n = 5$. 1. Calculate the arithmetic mean ($\bar{x}$): $$\bar{x} = \frac{6 + 9 + 11 + 10 + 12}{5} = \frac{48}{5} = 9.6$$ 2. Calculate absolute deviations from the mean $|x_i - \bar{x}|$: - $|6 - 9.6| = 3.6$ - $|9 - 9.6| = 0.6$ - $|11 - 9.6| = 1.4$ - $|10 - 9.6| = 0.4$ - $|12 - 9.6| = 2.4$ 3. Calculate sum of absolute deviations: $$\sum |x_i - \bar{x}| = 3.6 + 0.6 + 1.4 + 0.4 + 2.4 = 8.4$$ 4. Calculate Mean Deviation: $$\text{M.D.} = \frac{8.4}{5} = 1.68$$ Since $1.68$ is the mathematically correct value, which is closest to $1.67$, we select Option C. Hence, **Option C** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP Nov 18Question 3102 of 473

All Questions

The MD about the Mean for the data $\displaystyle 6,9,11,10,12$ is

Options

\displaystyle 1.47

\displaystyle 1.57

\displaystyle 1.67

\displaystyle 1.87

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

Correct Answer

✅ Option c — $\displaystyle 1.67$

All Options:

A $\displaystyle 1.47$
B $\displaystyle 1.57$
C $\displaystyle 1.67$
D $\displaystyle 1.87$

Detailed Solution & Explanation

We are given the observations:

\displaystyle 6, 9, 11, 10, 12

. The number of observations is

\displaystyle n = 5

. 1. Calculate the arithmetic mean (

\displaystyle \bar{x}

\bar{x} = \frac{6 + 9 + 11 + 10 + 12}{5} = \frac{48}{5} = 9.6

2. Calculate absolute deviations from the mean

\displaystyle |x_i - \bar{x}|

: -

\displaystyle |6 - 9.6| = 3.6

\displaystyle |9 - 9.6| = 0.6

\displaystyle |11 - 9.6| = 1.4

\displaystyle |10 - 9.6| = 0.4

\displaystyle |12 - 9.6| = 2.4

3. Calculate sum of absolute deviations:

\sum |x_i - \bar{x}| = 3.6 + 0.6 + 1.4 + 0.4 + 2.4 = 8.4

4. Calculate Mean Deviation:

\text{M.D.} = \frac{8.4}{5} = 1.68

Since

\displaystyle 1.68

is the mathematically correct value, which is closest to

\displaystyle 1.67

, we select Option C. 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 MD about the Mean for the data 6,9,11,10,12\displaystyle 6,9,11,10,126,9,11,10,12 is