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The Number of Telephone Calls Received at an Exchange in 245 Successive One-minute Intervals Are Shown in the Following Frequency Distribution: - Mathematics

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ConceptVariance and Standard Deviation Standard Deviation of a Discrete Frequency Distribution

Question

The number of telephone calls received at an exchange in 245 successive one-minute 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.

 

\[x_i\]
fi 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.

∴  \[\text{Median,} M = 4\]
\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| d_i \right| = \frac{1}{245} \times 366 = 1 . 493\]

 

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 32: Statistics
Ex. 32.2 | Q: 2 | Page no. 11
Solution The Number of Telephone Calls Received at an Exchange in 245 Successive One-minute Intervals Are Shown in the Following Frequency Distribution: Concept: Variance and Standard Deviation - Standard Deviation of a Discrete Frequency Distribution.
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