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Calculate the Mean Deviation from the Median of the Following Frequency Distribution:Heights in Inches585960616263646566no. of Students15203235352220108 - Mathematics

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ConceptVariance and Standard Deviation Standard Deviation of a Discrete Frequency Distribution

Question

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

Heights in inches 58 59 60 61 62 63 64 65 66
No. of students 15 20 32 35 35 22 20 10 8

Solution

In order to find the mean deviation from the median, we will first have to calculate the median.
M is the value of  x  corresponding to the cumulative frequency just greater than or equal to \[\frac{N}{2}\] .

 
\[x_i\]
fi Cumulative Frequency
 

\[\left| d_i \right| = \left| x_i - 61 \right|\]
 

\[f_i \left| d_i \right|\]
58 15 15 3 45
59 20 35 2 40
60 32 67 1 32
61 35 102 0 0
62 35 137 1 35
63 22 159 2 44
64 20 179 3 60
65 10 189 4 40
66 8 197 5 40
 
 

\[N = \Sigma f_i = 197\]
   
 

\[\sum^n_{i = 1} f_i \left| d_i \right| = 336\]
Here,

\[\frac{N}{2} = \frac{197}{2} = 98 . 5\]

The cumulative frequency just greater than 98.5 is 102. The corresponding value of x is 61.
Therefore, the median is 61.

\[MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| d_i \right| = \frac{1}{197} \times 336 = 1 . 7055\]

 

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APPEARS IN

 RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 32: Statistics
Ex. 32.2 | Q: 1 | Page no. 11
Solution Calculate the Mean Deviation from the Median of the Following Frequency Distribution:Heights in Inches585960616263646566no. of Students15203235352220108 Concept: Variance and Standard Deviation - Standard Deviation of a Discrete Frequency Distribution.
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