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Standard X

Mathematics

Cumulative Frequency Distribution of Less Than Type

Following is ...

Question

Following is the distribution of marks of 70 students in a periodical test:

Marks Number of students

Marks less than 10
Marks less than 20
Marks less than 30
Marks less than 40
Marks less than 50 3
11
28
48
70

Draw a cumulative frequency curve for the above data and find the median.

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Solution

$We plot the points A (10, 3), B(20,11), C(30,28), D(40,48) and E(50,70) . Join AB, BC, CD, DE and EA with a free hand to get the curve representing the' less than type' series .$

$From P(0,35), draw PQ ∥x - axis meeting the curve at Q. Draw QM⊥OX meeting the x-axis a t M. C learly, OM= 33.5 u nits. Hence, Median=33.5$

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Q. Following is the distribution of marks of 70 students in a periodical test:

Marks	Less than 10	Less than 20	Less than 30	Less than 40	Less than 50
Number of students	3	11	28	48	70

Draw a cumulative frequency for the above data.

For the following distribution draw a 'less than type' ogive and from the curve find the median.

Marks obtained	Less than 20	Less than 30	Less than 40	Less than 50	Less than 60	Less than 70	Less than 80	Less than 90	Less than 100
Number of students	2	7	17	40	60	82	85	90	100

Q. Convert the following data in a simple frequency distribution:

5 students obtained less than 3 marks

12 students obtained less than 6 marks

25 students obtained less than 9 marks

33 students obtained less than 12 marks

Q. The following table shows the marks scored by 80 students in an examination:

Marks	Less than 5	Less than 10	Less than 15	Less than 20	Less than 25	Less than 30	Less than 35	Less than 40
Number of students	3	10	25	49	65	73	78	80

Calculate the mean marks correct to 2 decimal places.

Q. Calculate the median from the following data:

Marks	Frequency
Less than 10	5
Less than 20	20
Less than 30	45
Less than 40	80
Less than 50	100
Less than 60	115
Less than 70	125
Less than 80	130

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Following is the distribution of marks of 70 students in a periodical test:

Marks Number of students

Marks less than 10
Marks less than 20
Marks less than 30
Marks less than 40
Marks less than 50 3
11
28
48
70

Draw a cumulative frequency curve for the above data and find the median.

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Marks	Number of students
Marks less than 10 Marks less than 20 Marks less than 30 Marks less than 40 Marks less than 50	3 11 28 48 70

Following is the distribution of marks of 70 students in a periodical test: Marks Number of students Marks less than 10 Marks less than 20 Marks less than 30 Marks less than 40 Marks less than 50 3 11 28 48 70 Draw a cumulative frequency curve for the above data and find the median.

WeplotthepointsA(10,3),B(20,11),C(30,28),D(40,48)andE(50,70) .JoinAB,BC,CD,DEandEAwithafreehandtogetthecurverepresentingthe'lessthantype'series. ​FromP(0,35),drawPQ ∥x-axismeetingthecurveatQ.DrawQM⊥OXmeetingthex-axisatM.Clearly,OM= 33.5units.Hence,Median=33.5

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Following is the distribution of marks of 70 students in a periodical test:

Marks Number of students

Marks less than 10
Marks less than 20
Marks less than 30
Marks less than 40
Marks less than 50 3
11
28
48
70

Draw a cumulative frequency curve for the above data and find the median.