Page 192 - Maths Skills - 8

190 Maths

INTRODUCTION
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 a data is to present the raw data consisting of separate entries called observations into
a methodical presentation and tabulation. The data can then be represented graphically or pictorially using various
tools like bar graph, histogram, pie chart, etc. In this chapter we will learn how to represent data using a bar graph,
pie/circle graph and many more.

GROUPING OF DATA

So far we have studied about ungrouped data, however when the number of observations is large, the data set can
be classified into respective groups to make it easier to analyse and present the data.
Presentation and classification of data in groups along with the frequency of each group is known as the frequency
distribution of grouped data.

Important Terms
● Class interval: Each group into which the raw data is condensed is known as the class interval.
● Class limit: The end numbers of a class interval are known as class limits. The smallest number of the data
set is the lower class limit and the largest is upper class limit.
● Class size: The difference between the upper and lower limit of a class is known as its class size.

● Class mark: The class mark is the mid point of a respective class interval.

(upper limit + lower limit)
Class mark =
2
Now, let us learn how to make groups of the data set as given below:

9, 16, 13, 7, 8, 4, 18, 10, 17, 18, 9, 12, 5, 9, 9, 16, 1, 8, 17, 1, 10, 5, 9, 11, 15, 6, 14, 9, 1, 12, 5, 16, 4, 16, 8, 15, 14, 17
We follow these Steps:

Step 1: Put the numbers in order, then find the smallest and largest values in your data, and calculate the range.
1, 1, 1, 4, 4, 5, 5, 5, 6, 7, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 16, 16, 17,
17, 17, 18, 18
The smallest value is 1.
The largest value is 18.
The range is 18 − 1 = 17.
Step 2: Now calculate an approximate group size, by dividing the range by the number of groups you would like
to have. Then round up the group size to a singular digit.

Let us say we want about 5 groups.

Divide the range by 5: i.e. 17 = 3.4
5
Then round that up to 4.
Step 3: Pick a starting value that is less than or equal to the smallest value. Try to make it a multiple of the group
size if possible.