Question

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

• A. \(\frac 47\)
• B. \(-\frac 47\)
• C. \(\frac {16}{7}\)
• D. \(-\frac {16}{7}\)

Answer 1

The Correct Option is C

The given data,
\(3, 5, 9,3,8,10,7\)
Arrange the data in ascending order,
\(3,3,5,7,8,9,10\)
No. of observations \(N= 7\) (Odd)
Then, Median M= \(\frac {7+1}{2}= 4\)^th term = \(7\)
Now mean deviation about median,
\(=\dfrac{∑|x_i−M|}{N}\)

\(=\frac {|3-7|+|3-7|+|5-7|+|7-7|+|8-7|+|9-7|+|10-7|}{7}\)

\(=\frac {4+4+2+0+1+2+3}{7}\)

\(=\frac {16}{7}\)

So, the correct option is (C): \(\frac {16}{7}\)