Construct a frequency distribution table for the numbers given below, using the class intervals 21 - 30 , 31 - 40 , … … , etc. 75 , 67 , 57 , 50 , 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 an ogive.

Plot the points ( 30 , 4 ) ( 40 , 13 ) ( 50 , 22 ) ( 60 , 29 ) ( 70 , 37 ) ( 80 , 40 ) and join then by free hand smooth curve in order to obtain an ogive C . I . Frequency C . F 21 - 30 4 4 31 - 40 9 13 41 - 50 9 22 51 - 60 7 29 61 - 70 8 37 71 - 80 3 40 Plot the points ( 30 , 4 ) , ( 40 , 13 ) , ( 50 , 22 ) , ( 60 , 29 ) , ( 70 , 37 ) , ( 80 , 40 ) and join them by free hand smooth curve.

Construct a frequency distribution table for the numbers given below, using the class intervals 21 - 30 , 31 - 40 , … … , etc. 75 , 67 , 57 , 50 , 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 an ogive.

Plot the points ( 30 , 4 ) ( 40 , 13 ) ( 50 , 22 ) ( 60 , 29 ) ( 70 , 37 ) ( 80 , 40 ) and join then by free hand smooth curve in order to obtain an ogive C . I . Frequency C . F 21 - 30 4 4 31 - 40 9 13 41 - 50 9 22 51 - 60 7 29 61 - 70 8 37 71 - 80 3 40 Plot the points ( 30 , 4 ) , ( 40 , 13 ) , ( 50 , 22 ) , ( 60 , 29 ) , ( 70 , 37 ) , ( 80 , 40 ) and join them by free hand smooth curve.

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.

HARD

10th ICSE

IMPORTANT

Earn 100

Construct a frequency distribution table for the numbers given below, using the class intervals $21 - 30, 31 - 40, \dots \dots,$ etc.

$75, 67, 57, 50, 26, 33, 44, 58, 67, 75, 78, 43, 41, 31, 21, 32, 40, 62, 54, 69, 48, 47, 51, 38, 39,$

$43, 61, 63, 68, 53, 56, 49, 59, 37, 40, 68, 23, 28, 36$ and $47$ .

Use the table obtained to draw an ogive.

Important Questions on Graphical Representation (Histograms and Ogives)

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 5

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

Question Image

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 5

Use this table to construct an ogive.

Question Image

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.

Construct a frequency distribution table for the numbers given below, using the class intervals 21-30,31-40,……,etc. 75,67,57,50,26,33,44,58,67,75,78,43,41,31,21,32,40,62,54,69,48,47,51,38,39, 43,61,63,68,53,56,49,59,37,40,68,23,28,36 and 47. Use the table obtained to draw an ogive.

Important Questions on Graphical Representation (Histograms and Ogives)

Learn and Prepare for any exam you want !