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

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 a histogram.

Since the data is given is raw form or ungrouped manner, so we first convert it into grouped form and the frequency distribution table for the given data is. 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 and the required histogram will be as

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

HARD

10th ICSE

IMPORTANT

Earn 100

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 $10$ $15$ $17$ $12$ $10$ $8$

Important Questions on Graphical Representation (Histograms and Ogives)

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	$0$	$17$	$32$	$37$	$53$	$58$	$65$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 4

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 a histogram.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 23 - Graphical Representation (Histograms and Ogives)>EXERCISE>Q 4

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.

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.

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

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

Important Questions on Graphical Representation (Histograms and Ogives)

Learn and Prepare for any exam you want !

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 $10$ $15$ $17$ $12$ $10$ $8$