Question
The number of telephone calls received at an exchange in 245 successive oneminute intervals are shown in the following frequency distribution:
Number of calls  0  1  2  3  4  5  6  7 
Frequency  14  21  25  43  51  40  39  12 
Compute the mean deviation about median.
Solution
We will first calculate the median.
\[x_i\]

f_{i}  Cumulative Frequency 
\[\left d_i \right = \left x_i  4 \right\]

\[f_i \left d_i \right\]

0  14  14  4  56 
1  21  35  3  63 
2  25  60  2  50 
3  43  103  1  43 
4  51  154  0  0 
5  40  194  1  40 
6  39  233  2  78 
7  12  245  3  36 
\[N = \Sigma f_i = 245\]

\[\sum^n_{i = 1} f_i \left d_i \right = 366\]

Here,
\[\frac{N}{2} = \frac{245}{2} = 122 . 5\]
The cumulative frequency just greater than 122.5 is 154 and the corresponding value of x is 4.
∴ \[\text{Median,} M = 4\]
∴ \[\text{Median,} M = 4\]
\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left d_i \right = \frac{1}{245} \times 366 = 1 . 493\]
Is there an error in this question or solution?
Solution The Number of Telephone Calls Received at an Exchange in 245 Successive Oneminute Intervals Are Shown in the Following Frequency Distribution: Concept: Variance and Standard Deviation  Standard Deviation of a Discrete Frequency Distribution.