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

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.
$\therefore \text{ Median }, M = 13$

$MD = \frac{1}{N} \sum^n_{i = 1} f_i \left| d_i \right|$
$= \frac{1}{50} \times 136$
$= 2 . 72$

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#### APPEARS IN

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

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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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