Mean Deviation

Q.

What are mean deviation and standard deviation?

Q.

The sum of the deviations of the variates from the arithmetic mean is always

1. $1$

2. $0$

3. $-1$

4. Real number

Q.

The mean deviation for n observations $x_1,x_2,....x_n$ from their mean $\overline{X}$ is given by

1. $\frac{1}{n}{\sum }_{i=1}^n(x_i-\overline{X})$

2. ${\sum }_{i=1}^n(x_i-\overline{X}{)}^2$

3. ${\sum }_{i=1}^n(x_i-\overline{X})$

4. $\frac{1}{n}{\sum }_{i=1}^n|x_i-\overline{X}|$

Q.

If a student scored $82$ points on a test where the mean score was $78.2$ and the standard deviation was $6.7$. the students $z$ score is .

Q.

The sum of the $n$terms of the series $\frac{1^2}{1}+\frac{(1^2+2^2)}{(1+2)}+\frac{(1^2+2^2+3^2)}{(1+2+3)}+\dots .$ is

1. $\frac{(n+1)(n+2)}{3}$

2. $\frac{n(n+2)}{3}$

3. $\frac{n(n+1)}{3}$

4. none of these

Q. The sum of the squares of deviations of a set of values is minimum when taken about

1. AM
2. GM
3. HM
4. Medium

Q. What is the formula coefficient of variation?

Q. If the mean and standard deviations of $100$ observations $x_1,x_2,...,x_{100}$ are $5$ and $4$ respectively, then the mean of $(x_1+1{)}^2,(x_1+1{)}^2,...,(x_{100}+1{)}^2$ is

1. $51$
2. $52$
3. $151$
4. $152$

Q.

If $\mu$ is the mean of a distribution, then $\sum f_i(y_i-\mu )$ is equal to

1. mean deviation

2. standard deviation

3. 0

4. None of these

Q. If the sum of the deviations of $50$ observations from $30$ is $50$, then the mean of these observations is:

1. $50$
2. $51$
3. $30$
4. $31$

Q.

The mean deviation from the mean for the set of observations – 1, 0, 4 is

1. greater than 2.5
2. greater than 4.9
3. less than 3
4. less than 1

Q.

Find the sum of the series $1·n+2(n-1)+3(n-2)+...+(n-1)2+n·1$

Q. Find the equation of a line in
$\left(a\right)$ vector and
$\left(b\right)$ Cartesian form which joins the points whose position vector are $\hat{i}+2\hat{j}-3\hat{k}$ and $2\hat{i}+\hat{j}-\hat{k}$

Q. A line passes through the point with position vector $3\hat{i}-4\hat{j}+5\hat{k}$ and is in the direction of $\hat{i}+2\hat{j}-3\hat{k}$ find the equation of the line in vector and Cartesian from.

Q.

The mean deviation of the variates 40, 62, 68, 76, 54 from their arithmetic mean is

1. 9.4

2. 10

3. 11

4. 10.4

Q.

Given n observations x₁, x₂ ......x_n and their central tendency a. Find the mean deviation about a.

1. a and b

2. M.D(a) = $\frac{\sum _{i=1}^n|x_i-a|}{n}$

3. M.D(a) = $\frac{\sum _{i=1}^n{x}_i-a}{n}$

4. M.D(a) = $\sum _{i=1}^n{x}_i-a$

Q. A scientist is weighing each of $30$ fishes. Their mean weight worked out is $30gm$ and a standard deviation of $2gm$. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by $2gm$. The correct mean and standard deviation of fishes are :

1. $28,2$
2. $32,2$
3. $28,4$
4. $32,4$

Q.

Which of the following defines mean deviation?

1. Mean of deviations of observations from central value.

2. Mean of absolute deviations of observations from central value.

3. Mean of the observations in the data set

4. Mean of deviations about most occurring value

Q. If the sum of the deviations of $50$ observations from $30$ is $50$, then the mean of these observations is:

1. $50$
2. $51$
3. $30$
4. $31$

Q.

The mean deviation of the variates 40, 62, 68, 76, 54 from their arithmetic mean is

1. 9.4

2. 10

3. 11

4. 10.4

Q.

If $\mu$ is the mean of a distribution, then $\sum f_i(y_i-\mu )$ is equal to

1. mean deviation

2. standard deviation

3. 0

4. None of these

Q.

Which of the following defines mean deviation?

1. Mean of the observations in the data set

2. Mean of deviations about most occurring value

3. Mean of absolute deviations of observations from central value.

4. Mean of deviations of observations from central value.

Q. Find the cartesion equation of the plane passing through the point $(-2,1,3)$ and perpendicular to the vector $3i+j+5k.$

Q. The coefficient of mean deviation from median of observations $40,62,54,90,68,76$ is

1. $2.16$
2. $0.2$
3. None of these
4. $5$

Q. Which of the following measure of dispersion is based on absolute deviations?

1. Range
2. SD
3. Mean Deviation
4. Quartile Deviation

Q. Find the mean and variance for the data

$x_i$	6	10	14	18	24	28	30
$f_i$	2	4	7	12	8	4	3