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Home » Use graph paper for this question. The following table shows the weights in gm of a sample of 100 potatoes taken from a large consignment:
Use graph paper for this question. The following table shows the weights in gm of a sample of 100 potatoes taken from a large consignment:
CBSE | Class 10 | Exercise 1 | Exercise 1 | Maths | Measures of Central Tendency | Measures of Central Tendency | ML Aggarwal
Use graph paper for this question. The following table shows the weights in gm of a sample of 100 potatoes taken from a large consignment:
Weight (gm) 50-60 60-70 70-80 80-90 90-100 100-110 110-120 120-130
Frequency 8 10 12 16 18 14 12 10

(i) Calculate the cumulative frequencies. 

(ii) Draw the cumulative frequency curve and from it determine the median weight of the potatoes. (1996)

Solution:

(i)We write the given data in cumulative frequency table.

Marks frequency f Cumulative frequency c.f
50-60 8 8
60-70 10 18
70-80 12 30
80-90 16 46
90-100 18 64
100-110 14 78
110-120 12 90
120-130 10 100

(ii)To represent the data in the table graphically, we mark the upper limits of the class intervals on

the horizontal axis (x-axis) and their corresponding cumulative frequencies on the vertical axis ( y-axis),

Plot the points (60, 8), (70, 18), (80, 30), (90, 46), (100, 64), (110, 78), (120, 90) and (130, 100) on the graph.

Join the points with the free hand. We get an ogive as shown:

Here n = 100 which is even.

So median = ( n/2 th term)

= (100/2 th term)

= (50 th term)

Now mark a point A (50) on the Y-axis and from A draw a line parallel to X-axis meeting the curve at P. From P, draw a perpendicular on x-axis meeting it at Q.

Q is the median.

Q = 93 gm.

Hence the median is 93.

 

i

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