Graphical Representation Mathematics - Graphical Representation

The following table shows the distribution of the heights of a group of factory workers:

Ht. (cm)	150 - 155	155 – 160	160 - 165	165 – 170	170 – 175	175 - 180	180 – 185
No of workers:	6	12	18	20	13	8	6

(i) Determine the cumulative frequencies.
(ii) Draw the ‘less than’ cumulative frequency curve on graph paper. Use 2 cm = 5 cm height on one axis and 2 cm = 10 workers on the other.

Draw a cumulative frequency curve (ogive) for the following distributions:

Class Interval	10 – 15	15 – 20	20 – 25	25 – 30	30 – 35	35 – 40
Frequency	10	15	17	12	10	8

Construct a frequency distribution table for each of the following distributions.

Marks (more than)	0	10	20	30	40	50	60	70	80	90	100
Cumulative frequency	100	87	65	55	42	36	31	21	18	7	0

Construct a frequency distribution table for each of the following distributions

Marks (less than)	0	10	20	30	40	50	60	70	80	90	100
Cumulative frequency	0	7	28	54	71	84	105	147	180	196	200

Use graph paper for this question.
The table given below shows the monthly wages of some factory workers
(i) Using the table, calculate the cumulative frequencies of workers
(ii) Draw a cumulative frequency curve.
Use 2 cm = ₹ 500, starting the origin at ₹ 6500 on x-axis, and 2 cm = 10 workers on the y – axis.

Wages (in Rs)	6500-7000	7000-7500	7500-8000	8000-8500	8500-9000	9000-9500	9500-10000
No of workers	10	18	22	25	17	10	8

Class mark	12.5	17.5	22.5	27.5	32.5	32.5	42.5
Frequency	12	17	22	27	30	21	16

(a) From the distribution, given above, construct a frequency table.
(b) Use the table obtained in part (a) to draw: (i) a histogram, (ii) an ogive

Use the information given in the adjoining histogram to construct a frequency table.
Use this table to construct an ogive.

Construct a frequency distribution table for the numbers given below, using the class intervals
21 – 30, 31 – 40 ………… etc.
75, 65, 57, 26, 33,44, 58, 67, 75, 78, 43, 41, 31, 21, 32, 40, 62, 54, 69, 48, 47, 51, 38, 39, 43, 61, 63, 68, 53, 56, 49, 59, 37, 40, 68, 23, 28, 36 and 47.
Use the table obtained to draw: (1) a histrogram (2) an ogive

Draw a cumulative frequency curve (ogive) for each of the following distributions:

Class Interval	10 – 19	20 – 29	30 – 39	40 – 49	50 – 59
Frequency	23	16	15	20	12

Draw a cumulative frequency curve (ogive) for the following distributions:

Class Interval	10 – 15	15 – 20	20 – 25	25 – 30	30 – 35	35 – 40
Frequency	10	15	17	12	10	8

The following table shows the distribution of the heights of a group of factory workers:

Ht. (cm)	150 - 155	155 – 160	160 - 165	165 – 170	170 – 175	175 - 180	180 – 185
No of workers:	6	12	18	20	13	8	6

(i) Determine the cumulative frequencies.
(ii) Draw the ‘less than’ cumulative frequency curve on graph paper. Use 2 cm = 5 cm height on one axis and 2 cm = 10 workers on the other.

Use graph paper for this question.
The table given below shows the monthly wages of some factory workers
(i) Using the table, calculate the cumulative frequencies of workers
(ii) Draw a cumulative frequency curve.
Use 2 cm = ₹ 500, starting the origin at ₹ 6500 on x-axis, and 2 cm = 10 workers on the y – axis.

Wages (in Rs)	6500-7000	7000-7500	7500-8000	8000-8500	8500-9000	9000-9500	9500-10000
No of workers	10	18	22	25	17	10	8

Draw an ogive for each of the following distributions:

Age in years (less than)	10	20	30	40	50	60	70
Cumulative frequency	0	17	32	37	53	58	65

Draw an ogive for each of the following distributions:

Marks obtained	Less than 10	Less than 20	Less than 30	Less than 40	Less than 50
No of students	8	25	38	50	67