Draw histograms for the following frequency distributions: Class interval 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Frequency 12 20 26 18 10 6

Starting from 0 , mark 10 , 20 , 30 , 40 , 50 and 60 on x - axis at equal distance and 5 , 10 , 15 , 20 and 25 on y - axis at equal distance. Now, draw the rectangles to get required histograms:

Draw histograms for the following frequency distributions: Class intervals 10 - 16 16 - 22 22 - 28 28 - 34 34 - 40 Frequency 15 23 30 20 16

In the given frequency distribution, the first class interval is 10 - 16 . 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 10 and not at the origin itself.

Draw histograms for the following frequency distributions: Class interval 30 - 39 40 - 49 50 - 59 60 - 69 70 - 79 Frequency 24 16 09 15 20

In this case the class-interval are given in inclusive form. So, we have to convert them into exclusive form. Since the adjustment factor = 1 2 (difference between the upper unit of a class and the lower limit of next class) = 1 2 ( 40 - 39 ) = 0 . 5 ∴ To convert given class intervals in exclusive form subtract the adjustment factor from all the lower units and add it to all upper units. Therefore, by convert it into exclusive form the frequency table is given as: Exclusive C.I. form Frequency 29 . 5 - 39 . 5 24 39 . 5 - 49 . 5 16 49 . 5 - 59 . 5 09 59 . 5 - 69 . 5 15 69 . 5 - 79 . 5 20

Draw histograms for the following frequency distributions: Class mark 16 24 32 40 48 56 64 Frequency 8 12 15 18 25 19 10

Since the difference between the values of any consecutive class marks is 8 . therefore, subtract 8 2 = 4 from each class marks to get lower limit of corresponding class - interval and add 4 each to each class mark to get the upper limit. Then, the given frequency distribution will be of form Class marks C.I. Frequency 16 12 - 20 8 24 20 - 28 12 32 28 - 36 15 40 36 - 44 18 48 44 - 52 25 56 52 - 60 19 64 60 - 68 10

Draw a cumulative frequency curve (ogive) for each of 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 c . f table for the given distribution is as follows → C.I frequency c . f 10 - 15 10 10 15 - 20 15 25 20 - 25 17 42 25 - 30 12 54 30 - 35 10 64 35 - 40 8 72 Taking upper class units along x - axis and corresponding cumulative frequencies along y - axis mark the points ( 15 , 10 ) ( 20 , 25 ) ( 25 , 42 ) ( 30 , 54 ) ( 35 , 64 ) ( 40 , 72 ) Join the points marked by a free hand curve Plot the points ( 15 , 10 ) , ( 20 , 25 ) , ( 25 , 42 ) , ( 30 , 54 ) , ( 35 , 64 ) , ( 40 , 72 ) and join them by free hand smooth curve.

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

C.I. (Inclusive) C.I (Exclusive) Frequency c . f 10 - 19 9 . 5 - 19 . 5 23 23 20 - 29 19 . 5 - 29 . 5 16 39 30 - 39 29 . 5 - 39 . 5 15 54 40 - 49 39 . 5 - 49 . 5 20 74 50 - 59 49 . 5 - 59 . 5 12 86 Total 276 Plot the points ( 19 . 5 , 23 ) , ( 29 . 5 , 39 ) , ( 39 . 5 , 54 ) , ( 49 . 5 , 74 ) , ( 59 . 5 , 86 ) and joint them by free hand smooth curve.

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 Number of students. 8 25 38 50 67

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 Plot the points with abscissa as actual limits and ordinates as cumulative frequencies. (Draw and mark the horizontal and vertical axes.Take the cumulative frequencies along the y-axis (vertical axis) and the upper-class limits on the x-axis (horizontal axis).Against each upper-class limit, plot the cumulative frequencies.Connect the points with a continuous curve.)

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

From the given cumulative frequency distribution table, plot the points ( 10 , 0 ) ( 20 , 17 ) ( 30 , 32 ) ( 40 , 37 ) ( 50 , 53 ) ( 60 , 58 ) and ( 70 , 65 ) and join them 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 of the last class

HARD

10th ICSE

IMPORTANT

Earn 100

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

Important Questions on Graphical Representation (Histograms and Ogives)

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 1

Draw histograms for the following frequency distributions:

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Frequency	$12$	$20$	$26$	$18$	$10$	$6$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 1

Draw histograms for the following frequency distributions:

Class intervals	$10 - 16$	$16 - 22$	$22 - 28$	$28 - 34$	$34 - 40$
Frequency	$15$	$23$	$30$	$20$	$16$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 1

Draw histograms for the following frequency distributions:

Class interval	$30 - 39$	$40 - 49$	$50 - 59$	$60 - 69$	$70 - 79$
Frequency	$24$	$16$	$09$	$15$	$20$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 1

Draw histograms for the following frequency distributions:

Class mark	$16$	$24$	$32$	$40$	$48$	$56$	$64$
Frequency	$8$	$12$	$15$	$18$	$25$	$19$	$10$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 2

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

Class interval	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$
Frequency	$10$	$15$	$17$	$12$	$10$	$8$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 2

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	$23$	$16$	$15$	$20$	$12$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 3

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 $50$
Number of students.	$8$	$25$	$38$	$50$	$67$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 3

Draw an ogive for each of the following distributions:

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

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

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

Important Questions on Graphical Representation (Histograms and Ogives)

Learn and Prepare for any exam you want !

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