Find out median of the following series, using graphic technique:

Class Interval 40−45 45−50 50−55 55−60 60−65 65−70 70−75 75−80 80−85

Frequency 4 6 8 10 7 6 5 3 1

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Solution

Marks Cumulative Frequency

Less than 45
Less than 50
Less than 55
Less than 60
Less than 65
Less than 70
Less than 75
Less than 80
Less than 85 4
4 + 6 = 10
10 + 8 = 18
18 + 10 = 28
28 + 7 = 35
35 + 6 = 41
41 + 5 = 46
46 + 3 = 49
49 + 1 = 50

So, median is 58.5.

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Find the mean of the following using step deviation method.

Q. Find the median of the following data:

Weight (in kg)	40-45	45-50	50-55	55-60	60-65	65-70	70-75
Number of students	2	3	8	6	6	3	2

Q. The following table gives the weights of one hundred persons. Copute the coefficient of dispersion by the method of limits.

Class-interval	40−45	45−50	50−55	55−60	60−65	65−70	70−75	75−80	80−85	85−90
No. of persons	4	13	8	14	9	16	17	9	8	2

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

Weight (in kg)	40 − 45	45 − 50	50 − 55	55 − 60	60 − 65	65 − 70	70 − 75
Number of students	2	3	8	6	6	3	2

Find the mode for the following data.

$\begin{matrix} C l a s s i n t e r v e l & 35 - 45 & 45 - 55 & 55 - 65 & 65 - 75 & 75 - 85 F r e q u e n c y & 200 & 250 & 50 & 70 & 40 \end{matrix}$

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Class Interval	40−45	45−50	50−55	55−60	60−65	65−70	70−75	75−80	80−85
Frequency	4	6	8	10	7	6	5	3	1

Marks	Cumulative Frequency
Less than 45 Less than 50 Less than 55 Less than 60 Less than 65 Less than 70 Less than 75 Less than 80 Less than 85	4 4 + 6 = 10 10 + 8 = 18 18 + 10 = 28 28 + 7 = 35 35 + 6 = 41 41 + 5 = 46 46 + 3 = 49 49 + 1 = 50

Find out median of the following series, using graphic technique: Class Interval 40−45 45−50 50−55 55−60 60−65 65−70 70−75 75−80 80−85 Frequency 4 6 8 10 7 6 5 3 1

Marks Cumulative Frequency Less than 45 Less than 50 Less than 55 Less than 60 Less than 65 Less than 70 Less than 75 Less than 80 Less than 85 4 4 + 6 = 10 10 + 8 = 18 18 + 10 = 28 28 + 7 = 35 35 + 6 = 41 41 + 5 = 46 46 + 3 = 49 49 + 1 = 50 So, median is 58.5.

Find out median of the following series, using graphic technique:

Class Interval 40−45 45−50 50−55 55−60 60−65 65−70 70−75 75−80 80−85

Frequency 4 6 8 10 7 6 5 3 1

Marks Cumulative Frequency

Less than 45
Less than 50
Less than 55
Less than 60
Less than 65
Less than 70
Less than 75
Less than 80
Less than 85 4
4 + 6 = 10
10 + 8 = 18
18 + 10 = 28
28 + 7 = 35
35 + 6 = 41
41 + 5 = 46
46 + 3 = 49
49 + 1 = 50

So, median is 58.5.