Question

For the data set (10, 20, 30, 40, 50), what is the mean deviation about the median?

• A. 12
• B. 10
• C. 15
• D. 20

Answer 1

Answer: (A)

12

Answer 2

To find the mean deviation about the median for the given data set (10, 20, 30, 40, 50), follow these steps:

1. Arrange the data in ascending order:
   The given data is already in ascending order: {10, 20, 30, 40, 50}.

2. Find the median (M):
   The number of observations (n) is 5, which is an odd number.
   For an odd number of observations, the median is the $(\frac{n+1}{2})^{th}$ observation.
   Here, $n = 5$, so the median is the $(\frac{5+1}{2})^{th} = 3^{rd}$ observation.
   The 3rd observation in the ordered data set is 30.
   Therefore, Median (M) = 30.

3. Calculate the absolute deviations from the median: $|x_i - M|$ for each data point $x_i$.

   • For $x_1 = 10$: $|10 - 30| = |-20| = 20$
   • For $x_2 = 20$: $|20 - 30| = |-10| = 10$
   • For $x_3 = 30$: $|30 - 30| = |0| = 0$
   • For $x_4 = 40$: $|40 - 30| = |10| = 10$
   • For $x_5 = 50$: $|50 - 30| = |20| = 20$

4. Sum the absolute deviations: $\sum |x_i - M|$
   Sum = $20 + 10 + 0 + 10 + 20 = 60$

5. Calculate the mean deviation about the median: M.D.(M) = $\frac{\sum |x_i - M|}{n}$
   M.D.(M) = $\frac{60}{5} = 12$

The mean deviation about the median is 12.