Mean Deviation

Q.

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

1. mean deviation

2. None of these

3. standard deviation

4. 0

Q. Find the mean deviation about the mean for the following data:

Marks obtained	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Number of students	$5$	$8$	$15$	$16$	$6$

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 group of $45$ house owners contributed money towards green environment of their street. The amount of money collected is shown in the table below.

Amount	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
No. of house owners	$2$	$7$	$12$	$19$	$5$

Calculate the variance and standard deviation.

1. $416,20.4$.
2. $6.76,6.06$.
3. $36.76,6.76$.
4. None of these

Q. If the standard deviation of $2x_i+3$ is 8, then the variance of $\frac{3x_i}{2}.$

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