Measure of Dispersion

Q.

Find domain and range of f(x) = - |x|

Q.

Find the mean deviation about the mean for the data.

Income per day	Number of persons
0-100	4
100-200	8
200-300	9
300-400	10
400-500	7
500-600	5
600-700	4
700-800	3

Q.

Find the mean, variance and standard deviation using short-cut method

Height in cms	No. of children
70-75	3
75-80	4
80-85	7
85-90	7
90-95	15
95-100	9
100-105	6
105-110	6
110-115	3

Q.

Find the mean and variance for the following frequency distribution.

Classes	0-10	10-20	20-30	30-40	40-50
Frequencies	5	8	15	16	6

Q.

Find the mean deviation about the mean for the data

xi	10	30	50	70	90
fi	4	24	28	16	8

Q. The mean deviation about the mean for the data {5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5}
is 0.

1. True
2. False

Q.

Find the mean and variance for the first n natural numbers

Q.

Find the mean deviation about the mean for the data.

xi	5	10	15	20	25
fi	7	4	6	3	5

Q.

From the data given below state which group is more variable, A or B?

Marks	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Group A	9	17	32	33	40	10	9
Group B	10	20	30	25	43	15	7

Q.

Find the mean and variance for the first n natural numbers

Q.

The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On rechecking, it was found that an observation 8 was incorrect. Calculate the correct mean and standard deviation in each of the following cases:

(i) If wrong item is omitted.

(ii) If it is replaced by 12.

Q.

The diameters of circles (in mm) drawn in a design are given below:

Diameters	No. of children
33-36	15
37-40	17
41-44	21
45-48	22
49-52	25

Q. The mean deviation of the series $a,a+d,a+2d+......,a+(2n-1)d,a+2nd$ about the mean is

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

Q.

The range of the data: $21,6,17,18,12,8,4,13$ is

1. $17$

2. $12$

3. $8$

4. $15$

Q. What is the mean deviation about the mean for the following continuous frequency distribution?
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 2-4& 5\\ 4-6& 6\\ 6-8& 3\\ 8-10& 1\end{array}$$

1. 2.12
2. 4.77
3. 1.33
4. 4.53

Q. The algebraic sum of deviations of ten observations about 15 is 70.The mean is

1. none of these
2. 25
3. 22
4. 20

Q.

Find the mean deviation about the mean for the data

4, 7, 8, 9, 10, 12, 13, 17

Q.

Find the mean deviation about the mean for the data

xi	5	10	15	20	25
fi	7	4	6	3	5

Q.

Which of the following defines Range of a given data set.

1. Minimum value

2. Most occurring value

3. Maximum value - minimum value

4. Maximum value

Q. Let r be the range and $S^2=\frac{1}{n-1}{\sum }_{i=1}^n(x_i-\overline{x}{)}^2$, where S is the S.D. of a set of observations $x_1,x_2.....x_n$, then

1. 
2. 
3. 
4. None of these

Q. Let r be the range and $S^2=\frac{1}{n-1}{\sum }_{i=1}^n(x_i-\overline{x}{)}^2$, where S is the S.D. of a set of observations $x_1,x_2.....x_n$, then

1. $S\le r\sqrt{\frac{n}{n-1}}$
2. $S=r\sqrt{\frac{n}{n-1}}$
3. $S\ge r\sqrt{\frac{n}{n-1}}$
4. None of these

Q. Which one of the following is a measure of dispersion?

1. Mode
2. Standard deviation
3. Mean
4. Median

Q. Which of the following are measures of dispersion?

1. Standard Deviation, Median, Range
2. Standard Deviation, Mode, Range
3. Standard Deviation, Variance, Range
4. Mean, Mode, Median

Q. The mean deviation about the mean for the data {1, 2, 3, -3, -2, -1} is .

1. 1.71
2. 2
3. \N
4. 4

Q. The difference between the maximum and the minimum obervations in data is called the ____________.

1. mean of the data
2. median of the data
3. range of the data
4. mode of the data

Q.

Find the mean deviation about the mean for the data

38, 70, 48, 40, 42, 55, 63, 46, 54, 44

Q.

Find the mean deviation about the mean for the data.

Income per day	Number of persons
0-100	4
100-200	8
200-300	9
300-400	10
400-500	7
500-600	5
600-700	4
700-800	3

Q. The mean deviation about the mean for the data {5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5}
is 0.

1. True
2. False

Q.

For the data $0,2,3,5,9,2$and $-7$

Range$=$____.

Q.

Which of the following defines Range of a given data set.

1. Most occurring value

2. Minimum value

3. Maximum value - minimum value

4. Maximum value