Question

The following set of data is given: 72, 72, 74, 80, 82, 82, 86, 88, 92, 92. The mean deviation from the median is

• A. 5
• B. 6
• C. 7
• D. 8
• E. 9

Hint:

When the median is one of the data points (or the average of two identical points), several deviations will be zero, which simplifies the addition. Always group identical values when summing to avoid errors.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Mean deviation from the median measures the average absolute distance of each data point from the median.

Step 2: Key Formula or Approach:
1. Find the median \(M\).
2. Calculate deviations \(|x_i - M|\) for each \(x_i\).
3. \(M.D.(M) = \frac{\sum |x_i - M|}{n}\).

Step 3: Detailed Explanation:
1. The data is already sorted: 72, 72, 74, 80, 82, 82, 86, 88, 92, 92.
Number of terms \(n = 10\).
Median \(M\) = average of 5th and 6th terms = \((82+82)/2 = 82\).
2. Calculate absolute deviations from 82: \[ |72-82|=10, |72-82|=10, |74-82|=8, |80-82|=2, |82-82|=0 \] \[ |82-82|=0, |86-82|=4, |88-82|=6, |92-82|=10, |92-82|=10 \]
3. Sum of deviations: \[ \sum = 10 + 10 + 8 + 2 + 0 + 0 + 4 + 6 + 10 + 10 = 60 \]
4. Mean Deviation: \[ M.D. = \frac{60}{10} = 6 \]

Step 4: Final Answer:
The mean deviation from the median is 6.