Page 317 - Start Up Mathematics_8 (Non CCE)

20 Frequency Distribution

and Bar Graph

We all know that data is the given or available information. Raw data is like an unsolved puzzle which makes no
meaningful impression at the first glance other than being a collection of information. So, the first step for
systematic investigation of data is to present the raw data consisting of separate
entries called observations into a methodical presentation and tabulation. The data Extension
can then be represented graphically or pictorially using various tools like bar graph, Raw data is also termed
histogram, pie chart, etc. In this chapter we will learn how to represent data using as ungrouped data.
a bar graph.

Presentation of Data
Raw data needs to be arranged in a meaningful format so that the salient features of the given information
can be evaluated and studied. It can be arranged in an ascending or descending order, which is then called an
array or arranged data.

Data is of two types:
(i) Discrete data: The data which can take only whole number values is called discrete data. For example,
number of students in different classes: 20, 25, 32, 40, etc.

(ii) Continuous data: The data which can take any value i.e., whole numbers or fractional numbers is
called continuous data. For example, height of students: 146 cm, 152.50 cm, 148.37 cm,
156.25 cm
Let’s learn the meaningful tabulated method of data presentation through the following example.

Given below are the marks obtained by 35 students out of 100 in an examination, arranged in ascending
order:
8, 8, 19, 19, 22, 27, 27, 27, 35, 36, 39, 46, 46, 46, 46, 46, 48, 52, 56, 56, 56, 56, 60, 60, 65, 73, 73, 73, 85,
85, 87, 87, 87, 98, 98
Before we tabulate this data, let’s learn the following terms:
1. Range: The difference between the greatest and the smallest values in the set of observations is called
the range.

For example, in the above data, range of marks = 98 – 8 = 90
2. Frequency: Sometimes, observations can be too many and it becomes a cumbersome and tedious task to
arrange the terms in ascending or descending order. To arrange such data in a more meaningful way, count
the number of times a particular observation occurs and tabulate it. Frequency is defined as the number
of times a particular observation occurs in a data.

For example, in the above data 56 marks occur 4 times, so the frequency of the observation 56 is 4.
3. Tally marks: To avoid errors in counting large number of observations, vertical bars or lines called tally
marks are used to mark the frequencies. The symbol | is used to mark each frequency. Tally marks are
recorded in groups of 5. The fifth tally mark is drawn by crossing the first four tally marks diagonally
like .

Now let’s arrange the above data.