Question

If the mean of 4, 7, 2, 8, 6 and \( k \) is 7. Then the mean deviation from the mean of these observations is

• A. 5
• B. 3
• C. 1
• D. 8

Hint:

The mean deviation is calculated as the average of the absolute deviations from the mean.

Answer 1

The Correct Option is B

Step 1: Calculate the value of \( k \).
We are given that the mean of the observations is 7. The mean is calculated by dividing the sum of the observations by the total number of observations. We have 6 observations in total, so the mean is:
\[ \frac{4 + 7 + 2 + 8 + 6 + k}{6} = 7 \]
Simplifying the equation: \[ \frac{27 + k}{6} = 7 \]
Multiplying both sides by 6:
\[ 27 + k = 42 \] Solving for \( k \): \[ k = 15 \]

Step 2: List the observations.
The observations are now: 4, 7, 2, 8, 6, and 15.

Step 3: Calculate the mean of the observations.
The mean is given as 7, as stated in the problem.

Step 4: Calculate the deviations from the mean.
Now, we calculate the absolute deviations of each observation from the mean 7:
\[ |4 - 7| = 3, \quad |7 - 7| = 0, \quad |2 - 7| = 5, \quad |8 - 7| = 1, \quad |6 - 7| = 1, \quad |15 - 7| = 8 \]

Step 5: Calculate the mean deviation.
The mean deviation is the average of these absolute deviations: \[ \text{Mean deviation} = \frac{3 + 0 + 5 + 1 + 1 + 8}{6} = \frac{18}{6} = 3 \]

Step 6: Conclusion.
Therefore, the mean deviation from the mean of these observations is 3, and the correct answer is option (B).