The distribution of the heights of a group of a factory workers.

The following table shows the distribution of the heights of a group of factory workers.

(i) Determine the cumulative frequencies.
(ii) Draw the cumulative frequency curve on graph paper.
Use 2 cm = 5 cm height on one axis and 2 cm = 10 workers on the other.
(iii) From your graph, write down the median height in cm.

Solution:

Representing the distribution in cumulative
frequency distribution :

Here, n = 83 which is even.
Now taking points (155, 6), (160, 18), (165, 36), (170, 56),
(175, 69), (180, 77) and (185, 83) on the graph.

Now join them with free hand to form the ogive
or cumulative frequency curve as shown.
Here n = 83 which is odd
Median = th observation
= = 42th observation
Take a point A (42) on y-axis and from A,
draw a horizontal line parallel to x-axis meeting the curve at P.
From P draw a line perpendicular on the x-axis which meets it at Q.
∴Q is the median which is 166.5 cm. Ans.

More Solutions:

• Marks obtained by 200 students in an examination.
• The monthly income of a group of 320 employees.
• Record of the weight in kilograms of 200 students.
• The marks obtained by 100 students in a Mathematics
• The marks obtained by 120 students in a Mathematics
• The height of 160 students of a school.