Mean Deviation about Mean

Q. let $n$ be an odd natural number such that the variance of $1,2,3,4,\dots ,n$ is $14.$ Then $n$ is equal to

Q.

The mean deviation of the numbers 3, 4, 5, 6, 7 from the mean is

1. 25

2. 5

3. 1.2

4. 0

Q.

Consider three observations $a,b$ and $c$ such that $b=a+c$. If the standard deviation of $a+2,b+2,c+2$ is $d$, then which of the following is true?

1. $b^2=a^2+c^2+3d^2$

2. $b^2=3\left(a^2+c^2\right)-9d^2$

3. $b^2=3\left(a^2+c^2\right)+9d^2$

4. $b^2=3\left(a^2+c^2+d^2\right)$

Q.

A bats man scores runs in 10 innings as 38, 70, 48, 34, 42, 55, 63, 46, 54 and 44. The mean deviation about mean is

1. 8.6

2. 6.4

3. 10.6

4. 7.6

Q.

The mean deviation of the series a, a+d , a+2d, .... a+2n from its mean is

1. $\frac{(n+1)d}{2n+1}$

2. $\frac{n(n+1)d}{2n+1}$

3. $\frac{nd}{2n+1}$

4. $\frac{(2n+1)d}{n(n+1)}$

Q.

Compute mean deviation from mean of the following distribution :

$\begin{array}{ccccccccc}\text{Marks}& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80& 80-90\\ \text{No. of students}& 8& 10& 15& 25& 20& 18& 9& 5\end{array}$

Q. The mean deviation about the mean for the following data :
$5,6,7,8,6,9,13,12,15$ is :

1. $1.5$
2. $3.2$
3. $5$
4. $2.89$

Q. The mean of $5$ observations is $5$ and their variance is $12.4$. If three of the observations are $1,2$ and $6$; then the mean deviation from the mean of the data is:

1. $2.8$
2. $2.6$
3. $2.5$
4. $2.4$

Q. The variance of $3,6,9,\dots .,30$ is

1. $72.45$
2. $74.25$
3. $54.36$
4. $48.37$

Q.

How do you find the sum of deviations from mean?

Q.

The mean of four observations is $3$. If the sum of the squares of the observations is $48$, then their standard deviation is

1. $\sqrt{7}$

2. $\sqrt{2}$

3. $\sqrt{3}$

4. $\sqrt{5}$

Q.

Calculate the mean deviation from the mean for the following data :

(i) 4, 7, 8, 9, 10, 12, 13, 17

(ii) 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

(iii) 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

(iv) 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

(v) 57, 64, 43, 67, 49, 59, 44, 47, 61, 59

Q.

Find the mean deviation from the mean and from median of the following distribution :

$\begin{array}{cccccc}\text{Marks}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{No. of students}& 5& 8& 15& 16& 6\end{array}$

Q.

The lengths (in cm) of 10 rods in a shop are given below :

40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2

(i) Find mean deviation from median

(ii) Find mean deviation from the median also.

Q.

The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is

1. 2.57

2. 3

3. 3.57

4. 2

Q.

If the standard deviation of a variable $\mathrm{X}$ is $\sigma$, then the standard deviation of variable $\frac{\mathrm{aX}+\mathrm{b}}{\mathrm{c}}$; $a,b\in R$ is:

1. $a\sum _{}a+b$

2. $\left|\frac{\mathrm{a}}{\mathrm{c}}\right|\sigma$

3. $\left|a\right|\underset{}{\sum a}+b$

4. $a^2\sum _{}$

Q.

In question 1 (iii), (iv), (v) find the number of observations lying between $\overline{X}-M.D.$ and $\overline{X}-M.D,$ where M.D. is the mean deviation from the mean.

Q. If 5, x, 45 and y are in continued proportion, find the values of x and y.

Q. If the mean deviation about the median of the numbers $a,2a,....,50a$ is $50$. Then $|a|$ equals

1. $4$
2. $5$
3. $2$
4. $3$

Q.

Find the mean deviation from the mean for the following data :

(i) $\begin{array}{ccccccc}{x}_i& 5& 7& 9& 10& 12& 15\\ f_i& 8& 6& 2& 2& 2& 6\end{array}$

(ii) $\begin{array}{cccccc}{x}_i& 5& 10& 15& 20& 25\\ f_i& 7& 4& 6& 3& 5\end{array}$

(iii) $\begin{array}{cccccc}{x}_i& 10& 30& 50& 70& 90\\ f_i& 4& 24& 28& 16& 8\end{array}$

(iv) $\begin{array}{cccccc}\text{Size}& 20& 21& 22& 23& 24\\ \text{Frequency}& 6& 4& 5& 1& 4\end{array}$

(v) $\begin{array}{ccccccccc}\text{Size}& 1& 3& 5& 7& 9& 11& 13& 15\\ \text{Frequency}& 3& 3& 4& 14& 7& 4& 3& 4\end{array}$

Q. Find the mean deviation about median for the following data.
$18,23,9,11,26,4,14,21$

Q. The mean of $5$ observations is $5$ and their variance is $12.4$. If three of the observations are $1,2$ and $6$; then the mean deviation from the mean of the data is:

1. $2.8$
2. $2.6$
3. $2.4$
4. $2.5$

Q. If the mean deviation of the numbers $1,1+d,1+2d,\dots ,1+100d$ from their mean is $255$, then $|d|$ is equal to

1. $20$
2. $10.1$
3. $10$
4. $20.2$

Q.

You want to know the mean number of hour’s music students at your school practice each week. At each of three music classes you randomly survey $10$ students. Your results are shown. Use all three samples to make one estimate for the mean number of hour’s music students practice each week

$$\begin{gathered} \mathit{H}\mathit{o}\mathit{u}\mathit{r}\mathit{s}\mathbf{}\mathit{P}\mathit{r}\mathit{a}\mathit{c}\mathit{t}\mathit{i}\mathit{s}\mathit{e}\mathit{d}\mathbf{}\mathit{E}\mathit{a}\mathit{c}\mathit{h}\mathbf{}\mathit{W}\mathit{e}\mathit{e}\mathit{k} \\ A:6,5,5,6,4,6,8,5,2,6 \\ B:0,6,6,5,4,5,6,3,4,9 \\ C:4,5,6,4,3,2,2,3,12,1 \end{gathered}$$

Q. If variance of the first $n$ natural numbers is $10,$ then the value of $n$ is

Q. Find the mean deviation about the median for the following data.
$13,17,16,11,13,10,16,11,18,12,17$

Q. The range of numbers $x_1,x_2,x_3,x_4,x_5$ is $r$ where $x_i<x_{i+1}$. If each number is multiplied by $p(p>0)$ and then $k$ is subtracted from each number, then the range of new numbers is

1. $pr$
2. $pr-k$
3. $p$
4. $p(r-k)$

Q.

Find the mean deviation from the mean for the following data :

(i) $\begin{array}{ccccccccc}\text{Classes}& 0-100& 10-200& 200-300& 300-400& 400-500& 500-600& 600-700& 700-800\\ \text{Frequencies}& 4& 8& 9& 10& 7& 5& 4& 3\end{array}$

(ii) $\begin{array}{ccccccc}\text{Classes}& 95-105& 105-115& 115-125& 125-135& 135-145& 145-155\\ \text{Frequencies}& 9& 13& 26& 26& 30& 12\end{array}$

(iii) $\begin{array}{ccccccc}\text{Classes}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Frequencies}& 6& 8& 14& 16& 4& 2\end{array}$

Q. The Mean deviation about A.M. of the numbers $3,4,5,6,7$ is :

1. $25$
2. $5$
3. $1.2$
4. $0$

Q. Find the mean deviation about mean and median for the following data.

$CI$	$5-10$	$10-15$	$15-20$	$20-25$	$25-30$
$f$	$5$	$12$	$3$	$11$	$9$