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: Write the given observations.
The five numbers are:
\[ 2,\ 4,\ 6,\ 8,\ 10 \] We need to find the mean deviation from the mean.

Step 2: Find the arithmetic mean.
The mean is given by:
\[ \bar{x}=\frac{\text{sum of observations}}{\text{number of observations}} \] So,
\[ \bar{x}=\frac{2+4+6+8+10}{5} \] \[ \bar{x}=\frac{30}{5}=6 \]

Step 3: Find the deviation of each observation from the mean.
Now subtract the mean \(6\) from each observation:
\[ 2-6=-4,\quad 4-6=-2,\quad 6-6=0,\quad 8-6=2,\quad 10-6=4 \]

Step 4: Take absolute values of the deviations.
For mean deviation, we take absolute deviations:
\[ |2-6|=4,\quad |4-6|=2,\quad |6-6|=0,\quad |8-6|=2,\quad |10-6|=4 \] Thus, the absolute deviations are:
\[ 4,\ 2,\ 0,\ 2,\ 4 \]

Step 5: Find the sum of the absolute deviations.
\[ 4+2+0+2+4=12 \]

Step 6: Divide by the total number of observations.
Mean deviation from mean is:
\[ \text{M.D.}=\frac{\sum |x_i-\bar{x}|}{n} \] So,
\[ \text{M.D.}=\frac{12}{5}=2.4 \]

Step 7: State the final answer.
Hence, the mean deviation from mean of the given numbers is:
\[ \boxed{2.4} \] which matches option \((1)\).