Statistics - Part III
: Given below are marks obtained by 50 students in
their History test. The
marks are out of 100. Find out how many students obtained more than 71 % of
10, 30, 2, 5, 45, 35, 55, 80, 40,
the lowest marks a student can get is 0, this will be one end of our lowest
class interval. 100 is the highest marks a student can get. Therefore, this
will be the highest end of our class interval. By the frequency distribution
that we learnt in the earlier section, we would have had 0 to 100 number of
rows. Instead, by using the class interval concept, we can make the
presentation of data more compact.
look at the data that is presented and what is expected out of the data. Our
main objective is to find how many students got more than 71 % marks. We can
have class intervals 0-5, 6-10, 11-15, and up to 95-100. Width of each
interval is 5 (except the first class interval, where the width is 6. Such
unevenness in class intervals, especially at the extreme ends is acceptable
in statistics). We can also
have a class interval which is broader 0-10, 11-20, 21-30 and up to 91-100.
data can be presented as below.
total number of students who have got more than 71 % marks is 8.
: In the frequency table given below is the weight of bags of
rice stored in a super market. Find
out how many bags of rice that are stored have weights less than 10 kg.
the table, you can clearly see that the number of bags of rice that are
stored in the super market that have weights less than 10 kg is
A class interval can also be represented by the mid point of the
class or the class mark. In the
last example, we can calculate the mid point of the class as follows.
the first class interval : the limits are 1 and 5.
mid point is calculated by
the mid pint of the class 1 to 5 is 3.
the mid point of other class intervals can be calculated.
point of a class interval is also known as class
frequency polygon is made as follows :
Example 3 : The frequency polygon shows the amount of milk consumed in milliliters consumed by a number of families per day. Find out how many families consume more than 3000 milliliters of milk per day.
the frequency polygon given, it is clearly depicted that the number of
families that consume more than 3000 milliliters of milk per day is 3.
More advanced students, can say that to calculate the number of families that consume more than 3000 milliliters of milk per day, we will have to calculate the area under the polygon after 3000 on the X-axis.
: Draw a frequency polygon of the data given in example 2.
mid point of the class on the X-axis and the frequency on the Y-axis. You
will get a set of points, Join the points one after another to
obtain the frequency polygon.