Question

For the ungrouped data set {2, 5, 8, 11}, the mean deviation about the median is:

• A. 4.5
• B. 3
• C. 4
• D. 2.5

Answer 1

Answer: (B)

3

Answer 2

To find the mean deviation about the median for the given ungrouped data set {2, 5, 8, 11}, follow these steps:

1. Arrange the data in ascending order:
   The given data is already in ascending order: {2, 5, 8, 11}.

2. Find the median (M):
   The number of observations (n) is 4, which is an even number.
   For an even number of observations, the median is the average of the $(\frac{n}{2})^{th}$ and $(\frac{n}{2} + 1)^{th}$ observations.
   Here, $n/2 = 4/2 = 2$. So, we need the 2nd and 3rd observations.
   The 2nd observation is 5.
   The 3rd observation is 8.
   Median (M) = $\frac{5 + 8}{2} = \frac{13}{2} = 6.5$.

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

   • For $x_1 = 2$: $|2 - 6.5| = |-4.5| = 4.5$
   • For $x_2 = 5$: $|5 - 6.5| = |-1.5| = 1.5$
   • For $x_3 = 8$: $|8 - 6.5| = |1.5| = 1.5$
   • For $x_4 = 11$: $|11 - 6.5| = |4.5| = 4.5$

4. Sum the absolute deviations: $\sum |x_i - M|$
   Sum = $4.5 + 1.5 + 1.5 + 4.5 = 12$

5. Calculate the mean deviation about the median: M.D.(M) = $\frac{\sum |x_i - M|}{n}$
   M.D.(M) = $\frac{12}{4} = 3$

The mean deviation about the median is 3.