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-bar): x-bar = 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: text{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.

Central Tendency & DispersionMTP 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

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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.

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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