Frequency Distributions

Q.

A pie chart is to be drawn for representing the following data
$\begin{array}{cc}\text{Items of expenditure}& \text{Number of families}\\ \text{Education}& 150\\ \text{Food and clothing}& 400\\ \text{House rent}& 40\\ \text{Electricity}& 250\\ \text{Miscellaneous}& 160\end{array}$
The value of the central angle for food and clothing would be

1. 
2. 
3. 
4. 

Q.

Find the mean deviation about median for the following data:

Marks	Number of girls
0-10	6
10-20	8
20-30	14
30-40	16
40-50	4
50-60	2

Q. Calculate mean deviation about median for the given data

Class	$0-10$	$10-20$	$20-30$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$5$	$4$	$3$	$2$	$2$	$1$	$1$

1. $2.3$
2. $11.3$
3. $12$
4. $15$

Q. Consider the frequency distribution of the given number
$\begin{array}{ccccc}Value:& 1& 2& 3& 4\\ Frequency:& 5& 4& 6& f\end{array}$
​If the mean is known to be 3, then the value of f is

1. 3
2. 7
3. 10
4. 14

Q.

Find the mean deviation about the median for the data

xi	15	21	27	30	35
fi	3	5	6	7	8

Q. In a class of $50$ students, the mean and variance of the marks scored in mathematics is $8.4$ and $20$ respectively. If there are $30$ boys in the class and their mean and variance of marks scored in mathematics is $8.25$ and $24$ respectively, then the variance of marks scored by the girls will be

1. $13.69$
2. $13.91$
3. $13.96$
4. $14.02$

Q.

Calculate the mean and median for the following continuous frequency distribution.

$$\begin{array}{cc}\text{Class}& f_i\\ 0-10& 6\\ 10-20& 8\\ 20-30& 20\\ 30-40& 25\\ 40-50& 15\\ 50-60& 10\\ 60-70& 4\end{array}$$

1. 34.25, 32.4
2. 34.20, 34
3. 34.20, 32.1
4. 34, 32.1

Q.

Calculate the mean and median for the following continuous frequency distribution.

$$\begin{array}{cc}\text{Class}& f_i\\ 0-10& 6\\ 10-20& 8\\ 20-30& 20\\ 30-40& 25\\ 40-50& 15\\ 50-60& 10\\ 60-70& 4\end{array}$$

1. 34.25, 32.4
2. 34.20, 34
3. 34.20, 32.1
4. 34, 32.1

Q.

Find the mean deviation about the median for the data.

xi	5	7	9	10	12	15
fi	8	6	2	2	2	6

Q. What is the median for the following set of data?
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 0-5& 2\\ 5-10& 3\\ 10-15& 5\\ 15-20& 16\\ 20-25& 14\\ 25-30& 10\end{array}$$

1. 19.69
2. 15.67
3. 20.11
4. 11

Q.

Calculate the mean deviation about median age for the age distribution of 100 persons given below:

Age	Number
16-20	5
21-25	6
26-30	12
31-35	14
36-40	26
41-45	12
46-50	16
51-55	9

Q. If for some $x\in R$, the frequency distribution of the marks by $20$ students in test is:

Marks	2	3	5	7
Frequency	$(x+1{)}^2$	$(2x-5)$	$x^2-3x$	$x$

then the mean of the marks is:

1. $2.8$
2. $3.2$
3. $2.5$
4. $3.0$

Q. If the frequencies of first four numbers out of 1, 2, 4, 6, 8 are 2, 3, 3, 2 respectively, then the frequency of 8 if their A.M. is 5, is

1. 5
2. 6
3. none of these
4. 4

Q. Consider the frequency distribution of the given number
$\begin{array}{ccccc}Value:& 1& 2& 3& 4\\ Frequency:& 5& 4& 6& f\end{array}$
​If the mean is known to be 3, then the value of f is

1. 10
2. 14
3. 7
4. 3

Q. What is the median for the following set of data?
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 0-5& 2\\ 5-10& 3\\ 10-15& 5\\ 15-20& 16\\ 20-25& 14\\ 25-30& 10\end{array}$$

1. 19.69
2. 15.67
3. 20.11
4. 11

Q. Given the mean and the median of a data, we can find the exact value of its mode.

1. True
2. False

Q. What is the mean of the following data?
$$\begin{array}{cc}\text{Value}& \text{Frequency}\\ 0-20& 2\\ 20-40& 3\\ 60-80& 4\\ 80-100& 1\end{array}$$

1. 37
2. 65
3. 48
4. 45

Q. Given the mean and the median of a data, we can find the exact value of its mode.

1. True
2. False

Q. Consider the frequency distribution of the given number
$\begin{array}{ccccc}Value:& 1& 2& 3& 4\\ Frequency:& 5& 4& 6& f\end{array}$
​If the mean is known to be 3, then the value of f is

1. 3
2. 7
3. 10
4. 14

Q. Given the mean and the median of a data, we can find the exact value of its mode.

1. True
2. False

Q. The mean and median of a distribution are 22.5 and 20 respectively. The mode is approximately .

1. 20
2. 12
3. 15
4. 5

Q. If for some $x\in R$, the frequrency distribution of the marks obtained by $20$ students in a test is :

Marks	$2$	$3$	$5$	$7$
Frequency	$(x+1{)}^2$	$2x-5$	$x^2-3x$	$x$

then the mean of the marks is :

1. $2.5$
2. $3.0$
3. $3.2$
4. $2.8$

Q. Find the mean age from the following frequency distribution:

Age (in years)	25-29	30-34	35-39	40-44	45-49	50-54	55-59
No. of person	4	14	22	16	6	5	3

Q. If for some $x\in R$, the frequrency distribution of the marks obtained by $20$ students in a test is :

Marks	$2$	$3$	$5$	$7$
Frequency	$(x+1{)}^2$	$2x-5$	$x^2-3x$	$x$

then the mean of the marks is :

1. $2.5$
2. $3.2$
3. $3.0$
4. $2.8$

Q.

A pie chart is to be drawn for representing the following data
$\begin{array}{cc}\text{Items of expenditure}& \text{Number of families}\\ \text{Education}& 150\\ \text{Food and clothing}& 400\\ \text{House rent}& 40\\ \text{Electricity}& 250\\ \text{Miscellaneous}& 160\end{array}$
The value of the central angle for food and clothing would be

1. ${90}^{\circ }$

2. ${2.8}^{\circ }$

3. ${150}^{\circ }$

4. ${144}^{\circ }$

Q. Find the arithmetic mean of each of the following frequency distributions using step-deviation method:

Class	0-20	20-40	40-60	60-80	80-100	100-120	120-140
Frequency	12	18	15	25	26	15	9

Q. If for some $x\in R$, the frequrency distribution of the marks obtained by $20$ students in a test is :

Marks	$2$	$3$	$5$	$7$
Frequency	$(x+1{)}^2$	$2x-5$	$x^2-3x$	$x$

then the mean of the marks is :

1. $2.5$
2. $3.2$
3. $3.0$
4. $2.8$

Q. If the mean of the following frequency distribution is 54, find the value of p. [CBSE 2006C]

Class	0−20	20−40	40−60	60−80	80−100
Frequency	7	p	10	9	13

Q. Calculate the mean deviation about the mean for the following frequency distribution:

Class interval:	0–4	4–8	8–12	12–16	16–20
Frequency	4	6	8	5	2

Q. sum of deviation of a set of n values from 24 is 40 and from 26 is -40. then the mean is ?