Question

The mean deviation about the median for the data \(3,5,9,3,8,10,7\) is ?

• A. \(\dfrac{23}{7}\)
• B. \(\dfrac{4}{7}\)
• C. \(\dfrac{-4}{7}\)
• D. \(\dfrac{16}{7}\)
• E. \(\dfrac{17}{7}\)

Answer 1

The Correct Option is D

Given: Mean deviation about the median data= \(3,5,9,3,8,10,7\)

arranging it in ascending order =\(3,3,5,7,8,9,10\)

Hence observation(\(n\))=\(7\)

median=\(\dfrac{n+1}{2}=\dfrac{7+1}{2}=4\)

Now, the mean deviation about the median= \(\dfrac{|3−7∣+|3−7|+|5−7|+|7−7|+|8−7|+∣9−7∣+∣10−7∣​}{7}\)=\(\dfrac{16}{7}\)

Answer 2

First, we need to arrange the data in ascending order:

\[ 3, 3, 5, 7, 8, 9, 10 \]

There are 7 observations, so the median is the middle value, which is 7.

Next, we calculate the absolute deviations from the median (7):

\[ |3 - 7| = 4, \quad |3 - 7| = 4, \quad |5 - 7| = 2, \quad |7 - 7| = 0, \quad |8 - 7| = 1, \quad |9 - 7| = 2, \quad |10 - 7| = 3 \]

Now, sum the absolute deviations:

\[ 4 + 4 + 2 + 0 + 1 + 2 + 3 = 16 \]

The mean deviation about the median is the average of these absolute deviations:

\[ \text{Mean Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Number of observations}} = \frac{16}{7} \]

Therefore, the mean deviation about the median for the given data is \( \frac{16}{7} \).