Class mark 12 . 5 17 . 5 22 . 5 27 . 5 32 . 5 37 . 5 42 . 5 Frequency 12 17 22 27 30 21 16 From the distribution, given above, construct a frequency table.

Since the difference between the value of any consecutive class marks is 5 . Therefore, subtract 5 2 = 2 . 5 from each class mark to get lower limit of corresponding class-interval and add 2 . 5 each to each class-mark to get upper. Then the frequency distribution will be of form: Difference in consecutive class mark = 17 . 5 - 12 . 5 = 5 First class interval will be 10 - 15 and so on. Class Mark C . I Frequency C . F 12 . 5 10 - 15 12 12 17 . 5 15 - 20 27 29 22 . 5 20 - 25 22 51 27 . 5 25 - 30 27 78 32 . 5 30 - 35 30 108 37 . 5 35 - 40 21 129 42 . 5 40 - 45 16 145

Class mark 12 . 5 17 . 5 22 . 5 27 . 5 32 . 5 37 . 5 42 . 5 Frequency 12 17 22 27 30 21 16 Use the table obtained in part (a) to draw : (i) a histogram, (ii) an ogive.

Class Mark C . I Frequency C . F 12 . 5 10 - 15 12 12 17 . 5 15 - 20 27 29 22 . 5 20 - 25 22 51 27 . 5 25 - 30 27 78 32 . 5 30 - 35 30 108 37 . 5 35 - 40 21 129 42 . 5 40 - 45 16 145 In the given frequency distribution, the first class-interval is 10 - 15 therefore, the scale on x - axis starts at 10 for this, in general a kink (break) or a zig-zag curve is drawn near the origin to tell that the graph is drawn to scale beginning at 150 and not at the origin it self. Plot the points ( 15 , 12 ) , ( 20 , 29 ) , ( 25 , 51 ) , ( 30 , 78 ) , ( 35 , 108 ) , ( 40 , 129 ) , ( 45 , 145 ) and join then by free hand smooth curve in order to obtain an ogive since an ogive is always started from a point on x - axis representing the lower limit of the first class and is terminated at the upper limit of the last class

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 Determine the cumulative frequencies.

The C . f . table for the given frequency distribution is as follows → Height(in cm) Number of workers C.f. 150 - 155 6 6 155 - 160 12 18 160 - 165 18 36 165 - 170 20 56 170 - 175 13 69 175 - 180 8 77 180 - 185 6 83

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 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.

Height(in cm) Number of workers C.f. 150 - 155 6 6 155 - 160 12 18 160 - 165 18 36 165 - 170 20 56 170 - 175 13 69 175 - 180 8 77 180 - 185 6 83 Plot the point ( 155 , 6 ) ( 160 , 18 ) ( 165 , 36 ) ( 170 , 56 ) ( 175 , 69 ) ( 180 , 77 ) ( 185 , 83 ) and join these points by free hand smooth curve in order to obtain a less than type cumulative frequency curve.

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

The frequency distribution table for the given the given cumulative frequency distribution is as The C . F . table for the given frequency distribution is as follows → Marks (less than) C.F. frequency CF - F 1 0 - 10 7 7 10 - 20 28 21 20 - 30 54 26 30 - 40 71 17 40 - 50 84 13 50 - 60 105 21 60 - 70 147 42 70 - 80 180 33 80 - 90 196 16 90 - 100 200 4 Total 200

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 100 87 65 55 42 36 31 21 18 7 0

The frequency distribution table for the given the given cumulative frequency distribution is as Marks (more than) C.F. frequency 0 - 10 100 13 10 - 20 87 22 20 - 30 65 10 30 - 40 55 13 40 - 50 42 6 50 - 60 36 5 60 - 70 31 10 70 - 80 21 3 80 - 90 18 11 90 - 100 7 7 Total 100

HARD

10th ICSE

IMPORTANT

Earn 100

Use this table to construct an ogive.

Important Questions on Graphical Representation (Histograms and Ogives)

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 6

Class mark	$12.5$	$17.5$	$22.5$	$27.5$	$32.5$	$37.5$	$42.5$
Frequency	$12$	$17$	$22$	$27$	$30$	$21$	$16$

From the distribution, given above, construct a frequency table.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 6

Class mark	$12.5$	$17.5$	$22.5$	$27.5$	$32.5$	$37.5$	$42.5$
Frequency	$12$	$17$	$22$	$27$	$30$	$21$	$16$

Use the table obtained in part (a) to draw :
(i) a histogram,
(ii) an ogive.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 7

Use graph paper for this question.
The table given below shows the monthly wages of some factory workers.

Using the table, calculate the cumulative frequencies of workers.

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

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 7

Use graph paper for this question.
The table given below shows the monthly wages of some factory workers.

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

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 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 :	$6$	$12$	$18$	$20$	$13$	$8$	$6$

Determine the cumulative frequencies.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 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 :	$6$	$12$	$18$	$20$	$13$	$8$	$6$

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.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 9

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	$0$	$7$	$28$	$54$	$71$	$84$	$105$	$147$	$180$	$196$	$200$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 9

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	$100$	$87$	$65$	$55$	$42$	$36$	$31$	$21$	$18$	$7$	$0$

Use this table to construct an ogive.

Important Questions on Graphical Representation (Histograms and Ogives)

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