Question

The mean deviation from mean of the five numbers \(2,4,6,8,10\) is

• A. \(2.4\)
• B. \(3.6\)
• C. \(4.8\)
• D. \(6\)
• E. \(0\)

Hint:

Mean deviation from mean is found by taking the average of the absolute deviations from the arithmetic mean. Never forget to use absolute values.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Mean Deviation (MD) from the mean is a measure of dispersion. It is the average of the absolute differences between each data point and the mean of the data set.
Step 2: Key Formula or Approach:
1. Calculate the mean (\(\bar{x}\)) of the data set. \(\bar{x} = \frac{\sum x_i}{n}\). 2. For each data point \(x_i\), calculate the absolute deviation from the mean: \(|x_i - \bar{x}|\). 3. Calculate the mean of these absolute deviations. MD = \(\frac{\sum |x_i - \bar{x}|}{n}\).
Step 3: Detailed Explanation:
The given numbers are 2, 4, 6, 8, 10. The number of observations is n=5.
1. Calculate the mean (\(\bar{x}\)):
\[ \bar{x} = \frac{2+4+6+8+10}{5} = \frac{30}{5} = 6 \] 2. Calculate the absolute deviations from the mean:

\(|2 - 6| = |-4| = 4\)
\(|4 - 6| = |-2| = 2\)
\(|6 - 6| = |0| = 0\)
\(|8 - 6| = |2| = 2\)
\(|10 - 6| = |4| = 4\)
3. Calculate the mean deviation:
Sum of absolute deviations = \(4 + 2 + 0 + 2 + 4 = 12\).
\[ \text{MD} = \frac{\sum |x_i - \bar{x}|}{n} = \frac{12}{5} = 2.4 \] Step 4: Final Answer:
The mean deviation from the mean is 2.4. This corresponds to option (A).