Question

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 (gms)	Frequency
50 - 60	8
60 - 70	10
70 - 80	12
80 - 90	16
90 - 100	18
100 - 110	14
110 - 120	12
120 - 130	10

(i) Calculate the cumulative frequencies.
(ii) Draw the cumulative frequency curve and form it determine the median weights of the potatoes.

Answer 1

(i) The cumulative frequencies table is :

Weight (gm)	Number of potatoes (f)	Cummulative Frequency
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) Plotting the points (60, 8), (70, 18), (80, 30), (90, 46), (100, 64), (110, 78), (120, 90), (130, 100) and joining them by a free hand we get cummulative frequency curve as shown the figure. To complete it, we join the curve to the point (lower limit of the lowest class, 50) i.e., (50, 0).

The positive of median is given by `"n"/(2) = (100)/(2)` = 50.
On vertical axis form the mark of 50. Draw the horizontal line cutting the curve at a point for which the abscissa is 92 gms. Which is the value of the median.