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Byju's Answer

Standard IX

Mathematics

Frequency Polygon

In a certain ...

Question

In a certain colony, 40 households were selected. The data on monthly income (₹'000) is given below:

20 12 35 55 40 14 35 8 18 11

60 11 35 50 45 20 16 7 15 70

18 65 62 16 21 19 24 11 19 35

13 25 43 15 30 40 25 55 22 35

(i) Make a frequency distribution taking class interval of 10 marks. (Take first class interval as 0−10).
(ii) Draw a histogram and a frequency polygon form the frequency distribution.

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Solution

Class Interval Tally Frequency

0 − 10 2

10 − 20 14

20 − 30 7

30 − 40 6

40 − 50 4

50 − 60 3

60 −70 3

70 − 80 1

40

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Similar questions

Q. Following are the marks (out of 100) obtained by 50 students in statistics:

70	55	51	42	57	45	60	47	63	53
33	65	39	82	55	64	58	61	65	42
50	52	53	45	45	25	36	59	63	39
65	54	49	54	64	75	42	41	52	35
30	35	15	48	26	20	40	55	46	18

make a frequency distribution taking the first class interval as 0-10.

Q. Weight of 20 students is given in kilograms. Using class interval of 5, make a frequency distribution.

30	45	26	25	42	33	15	35	45	45
45	39	42	40	18	35	41	20	36	48

Q. Marks scored by 50 students are given below:

40	45	38	24	46	42	45	18	53	64
45	32	52	54	78	65	52	64	66	43
48	55	50	43	48	20	27	65	37	55
51	55	62	66	38	16	60	58	46	35
72	62	54	58	30	36	43	82	46	53

(a) Arrange the marks in ascending order.
(b) Represent the marks in the form of discrete frequency distribution.
(c) Construct an inclusive frequency distribution with first class as 10−19. Also construct class boundaries.
(d) Construct a frequency distribution with exclusive class-intervals, taking the lowest class as 10−20.
(e) Convert the exclusive series constructed in (d) into 'less than' and 'more than' cumulative frequency distribution.

Draw a histogram table for the following data: [4 MARKS]

$\begin{matrix} Class interval & 1 - 10 & 11 - 20 & 21 - 30 & 31 - 40 Frequency & 7 & 12 & 15 & 13 \end{matrix}$

Q. An economic survey revealed that 30 families in a town incur following expenditure in a day (rupees).

11	12	14	16	16	17	18	18	20	20	20	21	21	22	22
23	23	24	25	25	26	27	28	28	31	32	32	33	36	38

(i) Convert these data in the form of a frequency distribution, using the following class intervals.
10−14, 15−19, 20−24, 25−29, 30−34 and 35−39.
(ii) How many families spend more than 29 rupees a day?

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20	12	35	55	40	14	35	8	18	11
60	11	35	50	45	20	16	7	15	70
18	65	62	16	21	19	24	11	19	35
13	25	43	15	30	40	25	55	22	35

Class Interval	Tally	Frequency
0 − 10		2
10 − 20		14
20 − 30		7
30 − 40		6
40 − 50		4
50 − 60		3
60 −70		3
70 − 80		1
		40

70	55	51	42	57	45	60	47	63	53
33	65	39	82	55	64	58	61	65	42
50	52	53	45	45	25	36	59	63	39
65	54	49	54	64	75	42	41	52	35
30	35	15	48	26	20	40	55	46	18

40	45	38	24	46	42	45	18	53	64
45	32	52	54	78	65	52	64	66	43
48	55	50	43	48	20	27	65	37	55
51	55	62	66	38	16	60	58	46	35
72	62	54	58	30	36	43	82	46	53

11	12	14	16	16	17	18	18	20	20	20	21	21	22	22
23	23	24	25	25	26	27	28	28	31	32	32	33	36	38

20	12	35	55	40	14	35	8	18	11
60	11	35	50	45	20	16	7	15	70
18	65	62	16	21	19	24	11	19	35
13	25	43	15	30	40	25	55	22	35

70	55	51	42	57	45	60	47	63	53
33	65	39	82	55	64	58	61	65	42
50	52	53	45	45	25	36	59	63	39
65	54	49	54	64	75	42	41	52	35
30	35	15	48	26	20	40	55	46	18

40	45	38	24	46	42	45	18	53	64
45	32	52	54	78	65	52	64	66	43
48	55	50	43	48	20	27	65	37	55
51	55	62	66	38	16	60	58	46	35
72	62	54	58	30	36	43	82	46	53

11	12	14	16	16	17	18	18	20	20	20	21	21	22	22
23	23	24	25	25	26	27	28	28	31	32	32	33	36	38

Class Interval Tally Frequency 0 − 10 2 10 − 20 14 20 − 30 7 30 − 40 6 40 − 50 4 50 − 60 3 60 −70 3 70 − 80 1 40

Class Interval Tally Frequency

0 − 10 2

10 − 20 14

20 − 30 7

30 − 40 6

40 − 50 4

50 − 60 3

60 −70 3

70 − 80 1

40

20	12	35	55	40	14	35	8	18	11
60	11	35	50	45	20	16	7	15	70
18	65	62	16	21	19	24	11	19	35
13	25	43	15	30	40	25	55	22	35

70	55	51	42	57	45	60	47	63	53
33	65	39	82	55	64	58	61	65	42
50	52	53	45	45	25	36	59	63	39
65	54	49	54	64	75	42	41	52	35
30	35	15	48	26	20	40	55	46	18

40	45	38	24	46	42	45	18	53	64
45	32	52	54	78	65	52	64	66	43
48	55	50	43	48	20	27	65	37	55
51	55	62	66	38	16	60	58	46	35
72	62	54	58	30	36	43	82	46	53

11	12	14	16	16	17	18	18	20	20	20	21	21	22	22
23	23	24	25	25	26	27	28	28	31	32	32	33	36	38