Exercise 31.1
Page no 31.11
Type 1
Question 1
Find the mean deviation from the mean for the following data :
(i) $30,40,70,60,20,10,50$
(ii) $4,7,8,9,10,12,13,17$
(iii) $0,2,7,-5,8,11,4,-3$
(iv) $4.5,4.75,5,5.25,5.5,6.25,6.5,7.75,8.5$
Question 2
Find the mean deviation from the median for the following data :
(i) $22,24,30,27,29,31,25,41,42$ (ii) $7,3,8,11,2,9,4,14,10$
(iii) $34,66,30,38,44,50,40,60,42,51$
(iv) $3,9,21,12,5,3,18,4,7,10,19$
Question 3
The mean of $6,8,5,7, x$ and 4 is 7 . Find the mean deviation about median of these observations.
Question 4
The lengths (in $\mathrm{cm}$ ) of 10 rods in a shop are given below : $42.0,52.3,55.2,72.9,52.8,79.0,32.5,15.2,27.9,30.2$.
(i) Find the mean deviation from median.
(ii) Find the mean deviation from mean.
Type 2
Question 5
Find the mean deviation from the mean for the data in the following questions
$\begin{aligned}&\begin{array}{|c|c|c|c|c|c|c|c|}\hline \text { (i) } & x_{i} & 5 & 7 & 9 & 10 & 12 & 15 \\\hline & f_{i} & 8 & 6 & 2 & 2 & 2 & 6 \\\hline\end{array}\\&\begin{array}{|c|c|c|c|c|c|c|c|}\hline \text { (ii) } & x_{i} & 2 & 5 & 6 & 8 & 10 & 12 \\\hline & f_{i} & 2 & 8 & 10 & 7 & 8 & 5 \\\hline\end{array}\\&\begin{array}{|c|c|c|c|c|c|c|}\hline \text { (iii) } & x_{i} & 10 & 30 & 50 & 70 & 90 \\\hline & f_{i} & 4 & 24 & 28 & 16 & 8 \\\hline\end{array}\end{aligned}$
Question 6
Find the mean deviation from median for the following set of observations :
$\begin{aligned}&\begin{array}{|c|c|c|c|c|c|c|}\hline \text { (i) } & x_{i} & 15 & 21 & 27 & 30 & 35 \\\hline & f_{i} & 3 & 5 & 6 & 7 & 8 \\\hline\end{array}\\&\begin{array}{|c|c|c|c|c|c|c|c|c|}\hline \text { (ii) } & x_{i} & 5 & 7 & 9 & 11 & 13 & 15 & 17 \\\hline & f_{i} & 2 & 4 & 6 & 8 & 10 & 12 & 8 \\\hline\end{array}\end{aligned}$
Question 7
Calculate the mean deviation from the median of the following frequency distribution.
$\begin{array}{|l|c|c|c|c|c|c|}\hline \text { Age } & 15 & 13 & 17 & 16 & 18 & 20 \\\hline \text { No. of students } & 4 & 5 & 4 & 2 & 6 & 3 \\\hline\end{array}$
Type 3
Question 8
$\begin{aligned}&\text { Compute the mean deviation from the median of the following distribution : }\\&\begin{array}{|l|c|c|c|c|c|}\hline \text { Class } & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 \\\hline \text { Frequency } & 5 & 10 & 20 & 5 & 10 \\\hline\end{array}\end{aligned}$
Question 9
Find the mean deviation from mean and the coefficient of mean deviation of the following distribution.
$\begin{array}{|l|c|c|c|c|c|}\hline \text { Class } & 1-5 & 6-10 & 11-15 & 16-20 & 21-25 \\\hline \text { Frequency } & 8 & 5 & 20 & 7 & 10 \\\hline\end{array}$
Question 10
Find the mean deviation from the mean for the following observations.
$\begin{array}{|l|c|c|c|c|c|c|c|c|}\hline \text { (i) Class } & 0-100 & 100-200 & 200-300 & 300-400 & 400-500 & 500-600 & 600-700 &700-800 \\\hline \text { Frequency } & 4 & 8 & 9 & 10 & 7 & 5 & 4 & 3 \\\hline\end{array}$
$\begin{aligned}&\text { (ii) }\\&\begin{array}{|l|c|c|c|c|c|c|c|}\hline \text { Class } & 10-20 & 20-30 & 30-40 & 40-50 & 50-60 & 60-70 & 70-80 \\\hline \text { Frequency } & 2 & 3 & 8 & 14 & 8 & 3 & 2 \\\hline\end{array}\end{aligned}$
Question 11
$\begin{aligned}&\text { Find the mean deviation from the median of the following distribution }\\&\begin{array}{|l|c|c|c|c|c|}\hline \text { Class } & 20-30 & 30-40 & 40-50 & 50-60 & 60-70 \\\hline \text { Frequency } & 3 & 8 & 12 & 9 & 8 \\\hline\end{array}\end{aligned}$
$\begin{aligned}&\text { (ii) }\\&\begin{array}{|l|c|c|c|c|c|}\hline \text { Marks } & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 \\\hline \text { No. of students } & 5 & 8 & 15 & 16 & 6 \\\hline\end{array}\end{aligned}$
$\begin{aligned}&\text { (iii) }\\&\begin{array}{|l|c|c|c|c|c|}\hline \text { Class } & 0-6 & 6-12 & 12-18 & 18-24 & 24-30 \\\hline \text { Frequency } & 8 & 10 & 12 & 9 & 5 \\\hline\end{array}\end{aligned}$
Question 12
The height distribution of 100 children is as follows :
$\begin{array}{|l|c|c|c|c|c|c|}\hline \text { Height }(\text { in } \mathrm{cm}) & 95-105 & 105-115 & 115-125 & 125-135 & 135145 & 145-155 \\\hline \text { No, of students } & 9 & 13 & 26 & 30 & 12 & 10 \\\hline\end{array}$
Calculate the mean deviation from the mean height .
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