Question

Calculate percentage cumulative frequencies for the mothers' weight data shown and draw the percentage cumulative frequency curve. Half of the mothers weighed what weight (or more)? Note: If you are drawing this by hand, you should plot each cumulative frequency value against the lower boundary of its corresponding group. To plot the origin point, you have to imagine a fictitious group below your lowest group, whose cumulative frequency is 0. The largest (uppermost) cumulative frequency value should be plotted against the upper boundary of its group.

The weight (kg) at booking, of the mothers of the first 30 babies whose birthweights

64
105
50
61
63
50

84
60
56
79
48
60

50
55
50
63
80
54

120
74
60
71
43
55

78
95
46
90
47
63

Answer 1

#### By using Excel:

We obtained the cumulative percentage:

Class	Frequency(f)	cumulative frequency(cf)	Cumulative%=(cf/total)*100
40-50	4	4	13.33%
50-60	8	12	40.00%
60-70	8	20	66.67%
70-80	4	24	80.00%
80-90	2	26	86.67%
90-100	2	28	93.33%
100-110	2	30	100.00%
Total	30

The median weight of the mother is obtained by using the formula:

where,

L is the lower limit of median class. here 60-70 is the median class.

f0: cumulative frequency of the class preceding median class.

fm: frequency of median class.

h: class width.

Hence Half of the mothers weighed is less than 61.5Kg.