Question
Calculate the mean deviation about the median of the following frequency distribution:
x_{i}  5  7  9  11  13  15  17 
f_{i}  2  4  6  8  10  12  8 
Solution
We will first calculate the median for the data.
\[x_i\]

f_{i}  Cumulative Frequency 
\[\left d_i \right = \left x_i  13 \right\]

\[f_i \left d_i \right\]

5  2  2  8  16 
7  4  6  6  24 
9  6  12  4  24 
11  8  20  2  16 
13  10  30  0  0 
15  12  42  2  24 
17  8  50  4  32 
\[N = \Sigma f_i = 50\]

\[\sum^n_{i = 1} f_i \left d_i \right = 136\]

Here,
\[\frac{N}{2} = \frac{50}{2} = 25\]
The cumulative frequency just greater than 25 is 30 and the corresponding value of x is 13.
\[\therefore \text{ Median }, M = 13\]
\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left d_i \right\]
\[ = \frac{1}{50} \times 136\]
\[ = 2 . 72\]
Is there an error in this question or solution?
Solution Calculate the Mean Deviation About the Median of the Following Frequency Distribution:Xi57911131517fi246810128 Concept: Variance and Standard Deviation  Standard Deviation of a Discrete Frequency Distribution.