Page 198 - Maths Skills - 7

196 Maths

INTRODUCTION
In the previous class, we have learned to collect and tabulate data and put it in the form of bar graphs. Collection,
organisation and presentation of data is of great significance as it not only helps in analysis and interpretation but
important inferences can also be drawn from it.

In today’s world with easy access to data, there is hardly any branch of studies, be it Mathematics, Economics,
Science, Medicine, Psychology, etc. where statistical application does not play an important role. Scientists,
businessmen, researchers, meteorologists, economists, etc. with the help of various statistical tools decide the
future course of action and project estimates for future.
In this chapter, we shall learn about how to evaluate three representative values — mean, median and mode,
review the bar graphs and learn more about it.

DATA

A collection of numerical facts about a specific kind of information is called data. Here, each numerical fact is
called an observation. Data can be categorized as:

(i) Range: The difference between the highest and the lowest values of observations in a data is called the
range of the data.

(ii) Raw Data: The first hand information of observations is called raw data or ungrouped data.
(iii) Grouped Data: When the large amount of information collected is categorised into different classes it is
known as grouped data.

ARITHMETIC MEAN
Sum of all observations
The mean, average or arithmetic mean of the given observations is defined as: Mean = Number of observations
It is generally represented as x .
We sometimes come across statements like: this car gives an average of 13 km per litre; the average test score of
Rahul is 78; or the average height of an Indian male is 170 cm. Thus, an average is a number that is representative

of a group of data. There are four different types of measures of central tendency: the mean, the median, the mode
and the mid-range.
Let us now understand, what do these mean and how these yield different results for the same set of data.
Consider the following data:

The marks scored by 10 students of Class VII in Mathematics (out of 50) are:

49, 35, 15, 49, 0, 25, 45, 49, 25, 38 Absorbing Facts
Let us find the mean (arithmetic mean), median and mode of the data. Mean lies in between the greatest
and smallest observation.
The arithmetic mean x is given by:
Sum of all observations 49 + 35 + 15 + 49 + 0 + 25 + 45 + 49 + 25 + 38 330
x = = = = 33
Number of observations 10 10

Therefore, the mean, x is 33.

RANGE
The different between the highest and the lowest observations of a group of observation or data is called is range.

In other words, it can be defined as: Range = Highest observation – Lowest observation

For example, the marks scored by 10 students are 49, 35, 15, 49, 0, 25, 45, 25, 38, 49