Find the mean deviation about mean for the numbers: 2, 6, 7, 4, 8, 3

Option b: 2. Solution: We are given the observations: 2, 6, 7, 4, 8, 3 . The number of observations is n = 6 . 1. Calculate the arithmetic mean ( x ): x = 2 + 6 + 7 + 4 + 8 + 3/6 = 30/6 = 5 2. Calculate absolute deviations from the mean |xi - 5| : - |2 - 5| = 3 - |6 - 5| = 1 - |7 - 5| = 2 - |4 - 5| = 1 - |8 - 5| = 3 - |3 - 5| = 2 3. Calculate sum of absolute deviations: sum |xi - 5| = 3 + 1 + 2 + 1 + 3 + 2 = 12 4. Calculate Mean Deviation about Mean: M.D. = 12/6 = 2 Hence, Option B is the correct answer.

Find the mean deviation about mean for the numbers: $2, 6, 7, 4, 8, 3$

The correct answer is Option b: $2$. We are given the observations: $2, 6, 7, 4, 8, 3$. The number of observations is $n = 6$. 1. Calculate the arithmetic mean ($\bar{x}$): $$\bar{x} = \frac{2 + 6 + 7 + 4 + 8 + 3}{6} = \frac{30}{6} = 5$$ 2. Calculate absolute deviations from the mean $|x_i - 5|$: - $|2 - 5| = 3$ - $|6 - 5| = 1$ - $|7 - 5| = 2$ - $|4 - 5| = 1$ - $|8 - 5| = 3$ - $|3 - 5| = 2$ 3. Calculate sum of absolute deviations: $$\sum |x_i - 5| = 3 + 1 + 2 + 1 + 3 + 2 = 12$$ 4. Calculate Mean Deviation about Mean: $$\text{M.D.} = \frac{12}{6} = 2$$ Hence, **Option B** is the correct answer.

Measures of Central Tendency and DispersionMCQMTP March 21Question 3110 of 473

All Questions

Find the mean deviation about mean for the numbers: $\displaystyle 2, 6, 7, 4, 8, 3$

Options

\displaystyle 1

\displaystyle 2

\displaystyle 5

\displaystyle 6

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

Correct Answer

✅ Option b — $\displaystyle 2$

All Options:

A $\displaystyle 1$
B $\displaystyle 2$
C $\displaystyle 5$
D $\displaystyle 6$

Detailed Solution & Explanation

We are given the observations:

\displaystyle 2, 6, 7, 4, 8, 3

. The number of observations is

\displaystyle n = 6

. 1. Calculate the arithmetic mean (

\displaystyle \bar{x}

\bar{x} = \frac{2 + 6 + 7 + 4 + 8 + 3}{6} = \frac{30}{6} = 5

2. Calculate absolute deviations from the mean

\displaystyle |x_i - 5|

: -

\displaystyle |2 - 5| = 3

\displaystyle |6 - 5| = 1

\displaystyle |7 - 5| = 2

\displaystyle |4 - 5| = 1

\displaystyle |8 - 5| = 3

\displaystyle |3 - 5| = 2

3. Calculate sum of absolute deviations:

\sum |x_i - 5| = 3 + 1 + 2 + 1 + 3 + 2 = 12

4. Calculate Mean Deviation about Mean:

\text{M.D.} = \frac{12}{6} = 2

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.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central Tendency Fiscal Policy vs Monetary Policy: CA Foundation Economics

Ready to Master Measures of Central Tendency and Dispersion?

Practice all 473 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

Find the mean deviation about mean for the numbers: 2,6,7,4,8,3\displaystyle 2, 6, 7, 4, 8, 32,6,7,4,8,3