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

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

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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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