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Calculate the Mean Deviation About the Median of the Following Frequency Distribution:Xi57911131517fi246810128 - Mathematics

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ConceptVariance and Standard Deviation Standard Deviation of a Discrete Frequency Distribution

Question

Calculate the mean deviation about the median of the following frequency distribution:

xi 5 7 9 11 13 15 17
fi 2 4 6 8 10 12 8

Solution

We will first calculate the median for the data. 

 

 

\[x_i\]
fi 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?

APPEARS IN

 RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 32: Statistics
Ex. 32.2 | Q: 3 | Page no. 11
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.
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