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-bar): x-bar = 6 + 9 + 11 + 10 + 12/5 = 48/5 = 9.6 2. Calculate absolute deviations from the mean |xi - x-bar|: - |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-bar| = 3.6 + 0.6 + 1.4 + 0.4 + 2.4 = 8.4 4. Calculate Mean Deviation: text{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.

Central Tendency & DispersionMTP 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

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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.

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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