NCERT Class 9 Mathematics

256 MATHEMATICS

Frequency polygons can also be drawn independently without drawing
histograms. For this, we require the mid-points of the class-intervals used in the data.
These mid-points of the class-intervals are called class-marks.

To find the class-mark of a class interval, we find the sum of the upper limit and
lower limit of a class and divide it by 2. Thus,

Class-mark =

Upper limit + Lower limit

2

Let us consider an example.

Example 9 : In a city, the weekly observations made in a study on the cost of living
index are given in the following table:

Table 14.10

Cost of living index Number of weeks

140 - 150 5

150 - 160 10

160 - 170 20

170 - 180 9

180 - 190 6

190 - 200 2

Total 52

Draw a frequency polygon for the data above (without constructing a histogram).

Solution : Since we want to draw a frequency polygon without a histogram, let us find
the class-marks of the classes given above, that is of 140 - 150, 150 - 160,....

For 140 - 150, the upper limit = 150, and the lower limit = 140

So, the class-mark =

150 + 140

2

=

290

2

= 145.

Continuing in the same manner, we find the class-marks of the other classes as well.