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(A) The given observations are already in ascending order. Adding a column corresponding to cumulative frequencies $(c.f.)$ of the given data,we obtai

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$3.23$

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(A) The given observations are already in ascending order. Adding a column corresponding to cumulative frequencies $(c.f.)$ of the given data,we obtain the following table:						${x_i}$			${f_i}$			$c.f.$							$5$			$8$			$8$							$7$			$6$			$14$							$9$			$2$			$16$							$10$			$2$			$18$							$12$			$2$			$20$							$15$			$6$			$26$			Here,$N = \sum f_i = 26,$ which is even.Median is the mean of the $13^{th}$ and $14^{th}$ observations. Both of these observations lie in the cumulative frequency $14,$ for which the corresponding observation is $7.$$	herefore 	ext{Median} (M) = \frac{7 + 7}{2} = 7.$The absolute values of the deviations from median,i.e.,$|x_i - M|,$ are calculated as follows:						$x_i$			$|x_i - M|$			$f_i$			$f_i|x_i - M|$							$5$			$2$			$8$			$16$							$7$			$0$			$6$			$0$							$9$			$2$			$2$			$4$							$10$			$3$			$2$			$6$							$12$			$5$			$2$			$10$							$15$			$8$			$6$			$48$			$\sum f_i |x_i - M| = 16 + 0 + 4 + 6 + 10 + 48 = 84.$$	ext{Mean Deviation} (M) = \frac{1}{N} \sum f_i |x_i - M| = \frac{84}{26} \approx 3.23.$

Marks obtained	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
Number of students	$10$	$8$	$12$	$9$	$11$

Class interval	Frequency
$0-2$	$1$
$2-4$	$3$
$4-6$	$5$
$6-8$	$3$
$8-10$	$1$

Age (in years)	$16-20$	$21-25$	$26-30$	$31-35$	$36-40$	$41-45$	$46-50$	$51-55$
Number of persons	$5$	$6$	$12$	$14$	$26$	$12$	$16$	$9$

Find the mean deviation about the median for the data.

${x_i}$ $5$ $7$ $9$ $10$ $12$ $15$

${f_i}$ $8$ $6$ $2$ $2$ $2$ $6$

Similar Questions

$\begin{aligned} &\text{Find the mean deviation about the mean for the following data:} \\ &\begin{array}{|l|c|c|c|c|c|} \hline \text{Class Interval} & 0-6 & 6-12 & 12-18 & 18-24 & 24-30 \\ \hline \text{Frequency} & 1 & 2 & 3 & 2 & 1 \\ \hline \end{array} \end{aligned}$

Find the mean deviation about the mean for the following data:
Marks obtained $0-20$ $20-40$ $40-60$ $60-80$ $80-100$
Number of students $10$ $8$ $12$ $9$ $11$

The mean deviation about the mean for the following data is
Class interval Frequency
$0-2$ $1$
$2-4$ $3$
$4-6$ $5$
$6-8$ $3$
$8-10$ $1$

Calculate the mean deviation about the median age for the age distribution of $100$ persons given below:

Age (in years) $16-20$ $21-25$ $26-30$ $31-35$ $36-40$ $41-45$ $46-50$ $51-55$

Number of persons $5$ $6$ $12$ $14$ $26$ $12$ $16$ $9$

The mean deviation about the median of the discrete data $12, 15, 7, 4, 4, 15, 23, 14$ is

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Find the mean deviation about the median for the data. ${x_i}$ $5$ $7$ $9$ $10$ $12$ $15$ ${f_i}$ $8$ $6$ $2$ $2$ $2$ $6$