Question

The weight of 50 workers is given below:

Weight in Kg	50-60	60-70	70-80	80-90	90-100	100-110	110-120
No. of Workers	4	7	11	14	6	5	3

Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following:

1) The upper and lower quartiles.

2) If weighing 95 kg and above is considered overweight, find the number of workers who are overweight.

Answer 1

The cumulative frequency table of the given distribution table is as follows:

Weight in Kg	Number of workers	Cumulative frequency
50-60	4	4
60-70	7	11
70-80	11	22
80-90	14	36
90-100	6	42
100-110	5	47
110-120	3	50

The ogive is as follows:

Number of worker = 50

1) Upper quartile (Q3) = `((3 xx 50)/4)^"th"` term = `(37.5)^th` term = 92

Lower quartile (`Q_1`) = `(50/4)^"th"` term = `(12.5)^"th"` term = 71.1

2) Through mark of 95 on the x-axis, draw a vertical line which meets the graph at point C.

Then through point C, draw a horizontal line which meets the y-axis at the mark of 39

Thus, number of workers weighing 95 kg and above = 50 - 39 = 11