Frequency Distribution MATHEMATICS - Frequency Distribution

State the variable are continue and which are discrete:
Sizes of shoes sold in a shoe-store

State the variable are continue and which are discrete:
Time taken by runners in a race

State the variable are continue and which are discrete:
Distance travelled by a train

State the variable are continue and which are discrete:
Number of car-accidents in a city

State the variable are continue and which are discrete:
Number of patients in a hospital per day

Define the following term : Cumulative frequency of a class

Define the following term : Frequency of a class

Define the following term : True class-limits

Define the following term : Class-mark

Define the following term : Class-limits

Following data gives the number of children in 40 families :
1,2,6,5,1,3,2,6,2,3,4,2,0,4,4,3,2,2,0,0,1,2,2,4,4,3,2,1,0,5,1,2,4,3,4,1,1,6,2,2
Represent it in the form of a frequency distribution.

Convert the following frequency distribution to exclusive form :

Class-interval	Frequency
30-34	7
35-39	9
40-44	13
45-49	6
50-54	3
55-59	10

Use this table to find:
(i) The true class-limits of the fourth class-interval
(ii) The class-boundaries of the fifth class-interval
(iii) The class-mark of the third class-interval
(iv) The class-size of the sixth class-interval.

Construct a frequency table from the following data :

Age (in years)	Number of students
Less than 10	6
Less than 20	14
Less than 30	30
Less than 40	52
Less than 50	65
Less than 60	70

Construct a frequency distribution table from the following cumulative frequency distribution :

Class-interval	Cumulative frequency
0 - 8	8
8 - 16	21
16 - 24	26
24 - 32	33
32 - 40	42

Construct the cumulative frequency table from the frequency table given below :

Class-interval	0-6	6-12	12-18	18-24	24-30
Frequency	7	11	8	14	12

The marks obtained by 40 students of a class in an examination are given below Present the data in the form of a frequency distribution using equal class-size, or such class being 10-15 (15 not included).
3, 20, 13, 1, 21, 13, 3 23, 16, 13, 18, 12, 5, 12, 5, 24, 9, 2, 7, 18, 20, 3, 10, 12, 7, 18, 2, 5, 7, 10, 16, 8, 16, 17, 8, 23, 21, 6, 23, 15

The marks obtained by 35 students in an examination are given below :
370, 290, 318, 175, 170, 410, 378, 405, 380, 375, 315, 305, 325, 275, 241, 288, 261, 355, 402, 380, 178, 253, 428, 240, 210,175,154, 405, 380, 370, 306, 460, 328, 440, 425
From a cumulative frequency table with class intervals of length 50.

The weights in grams of 50 apples picked at random from a consignment are as follows : 131, 113, 82, 75, 204, 81, 84, 118, 104, 110, 80, 107, 111, 141, 136, 123, 90, 78, 90, 115, 110, 98, 106, 99, 107, 84, 76, 186, 82, 100, 109, 128, 115, 107, 115, 119, 93, 187, 139, 129, 130, 68, 195, 123, 125, 111, 92, 86, 70, 126
Form the grouped frequency table by dividing the variable range into intervals of equ width of 20 g.

The weekly wages (in rupees) of 30 workers in a factory are given below :
630, 635, 690, 610, 635, 636, 639, 645, 698, 690, 620, 660, 632, 633, 655, 645, 604, 608, 612, 640, 685, 635, 636, 678, 640, 668, 690, 606, 640, 690
Represent the data in the form of a frequency distribution with class size 10.

Convert the following frequency distribution to exclusive form :

Class-interval	Frequency
30 - 34	7
35 - 39	9
40 - 44	13
45 - 49	6
50 - 54	3
55 - 59	10

Use this table to find :
(i) The true class-limits of the fourth class-interval
(ii) The class-boundaries of the fifth class-interval
(iii) The class-mark of the third class-interval
(iv) The class-size of the sixth class-interval.

The following data gives the weights (in grams) of some marbles picked up randomly from 3 boxes. The data was presented in the tabular form as below :

Weight (in g)	No. of marbles
50-55	5
55-60	7
60-65	8
65-70	6
70-75	2
75-80	1
80-85	1

Based on the above information, answer the following questions:
Q.1. Class size of the given distribution is :
(a) 5 (b) 10 (c) 50 (d) 85
Q.2. Class mark of the 3rd class is :
(a) 60 (b) 65 (c) 125 (d) 62.5
Q.3. The number of marbles whose weight is more than or equal to 75 g is :
(a) 0 (b) 1 (c) 2 (d) 28
Q.4. The number of marbles whose weight is less than 70 g is :
(a) 26 (b) 28 (c) 4 (d) 2
Q.5. The class boundaries of the 7th class interval are :
(a) 80, 85 (b) 80.5, 85.5 (c) 79.5, 85.5 (d) 80, 85.5

To maintain the health report card in a hospital, the weights of new born babies are recorded on regular basis. During a week, the weights (in kg) of new borns were recorded as below: 2.7, 2.6, 3.1, 2.2, 2.4, 2.9, 3.0, 2.5, 2.8, 2.5, 2.8, 2.9, 2.2, 2.9, 2.7, 2.8, 2.3, 2.8, 2.1, 2.2

Based on the above information, answer the following questions :
Q.1. Range of the data is:
(a) 1 kg (b) 0.4 kg (c) 0.5 kg (d) 1.1 kg
Q.2. How many babies are born during the week?
(a) 10 (b) 16 (c) 17 (d) 20
Q.3. How many babies weigh less than 2.4 kg ?
(a) 7 (b) 6 (c) 5 (d) 4
Q.4. How many babies weigh more than 2.7 kg ?
(a) 10 (b) 9 (c) 8 (d) 7
Q.5. How many babies weigh 2.8 kg ?
(a) 4 (b) 5 (c) 6 (d) 3

Case Study II : The following data gives the weights (in grams) of some marbles picked up randomly from 3 boxes. The data was presented in the tabular form as below :

Weight (in g)	No. of marbles
50 - 55	5
55 - 60	7
60 - 65	8
65 - 70	6
70 - 75	2
75 - 80	1
80 - 85	1

Based on the above information, answer the following questions :
1. Class size of the given distribution is :
(a) 5 (b) 10 (c) 50 (d) 85
2. Class mark of the 3rd class is :
(a) 60 (b) 65 (c) 125 (d) 62.5
3. The number of marbles whose weight is more than or equal to 75 g is:
(a) 0 (b) 1 (c) 2 (d) 28
4. The number of marbles whose weight is less than 70 g is:
(a) 26 (b) 28 (c) 4 (d) 2
5. The class boundaries of the 7th class interval are :
(a) 80, 85 (b) 80.5, 85.5 (c) 79.5, 85.5 (d) 80, 85.5

Case Study I : To maintain the health report card in a hospital, the weights of new born babies are recorded on regular basis

During a week, the weights (in kg) of new borns were recorded as below :
2.7, 2.6, 3.1, 2.2, 2.4, 2.9, 3.0, 2.5, 2.8, 2.5, 2.8, 2.9, 2.2, 2.9, 2.7, 2.8, 2.3, 2.8, 2.1, 2.2
Based on the above information, answer the following questions :
1. Range of the data is :
(a) 1 kg (b) 0.4 kg (c) 0.5 kg (d) 1.1 kg
2. How many babies are born during the week?
(a) 10 (b) 16 (c) 17 (d) 20
3. How many babies weigh less than 2.4 kg?
(a) 7 (b) 6 (c) 5 (d) 4
4. How many babies weigh more than 2.7 kg?
(a) 10 (b) 9 (c) 8 (d) 7
5. How many babies weigh 2.8 kg?
(a) 4 (b) 5 (c) 6 (d) 3

The class mark of a class-interval is a. If its lower limit is a - b then its upper limit is :

Range of 14, 12, 17, 18, 16 and p is 20. If p > 0 then p =

The distribution of marks of students of a class in a test is shown in the table below.

Marks	Number of students
0 - 15	12
15 - 30	19
30 - 45	8
45 - 60	4

Which of the following statements are correct?
(i) We can definitely say that no one scored 60 marks.
(ii) The number of students who got at least 30 marks is 12.

Age of teachers of a school varies from 24 years to 72 years. Rishabh has to make a grouped frequency distribution table of age of teachers. Which among the following class intervals of age will be most appropriate to make meaningful conclusion in less time and effort?

The class-mark of the class-interval 9.5-19.5 is …………..

The class-mark of the class-interval 20-30 is …………..

Upper limit of the class-interval 16-20 is …………..

Lower-limit of the class-interval 24-30 is …………..

The mid-point of a class-interval is called the ………….. of the interval.