ICSE Class 8 Maths Statistics Chapter 01 Statistics

Statistics

Statistics is the science which deals with the collection, classification, analysis and interpretation of numerical data.

Classification Of Data

Data must be classified or arranged in a systematic way before they can be analysed or interpreted. Data that are not arranged in a systematic way are called unclassified data or raw data. It is quite impossible to analyse or interpret such data. For example, Table 1.1 shows the number of chocolates consumed by 40 students of a class in a day. Looking at it, one would not be able to draw any conclusions about the number of students who ate 3 chocolates or the number of students who did not eat any chocolate at all.

Table 1.1 Raw data

2, 0, 0, 1, 2, 3, 2, 1, 2, 0, 3, 1, 0, 2, 3, 4, 5, 1, 1, 4, 0, 2, 2, 3, 3, 2, 2, 1, 1, 0, 2, 3, 1, 1, 2, 1, 2, 3, 1, 2.

Arrayed Data

The simplest way to organise raw data is to arrange them in either ascending or descending order. Data arranged this way are called arrayed data.

Table 1.2 Arrayed data

0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 5

The data in Table 1.1 can be represented as arrayed data in either of the ways shown in Table 1.2 and 1.3. It should be obvious that Table 1.3 gives more precise information than Table 1.2.

Table 1.3 Arrayed data

Teacher's Note

When you look at your class test marks or a list of students' heights, the raw data seems confusing until it is organized - just like sorting your clothes by color makes it easier to find what you need.

Frequency Distribution Table

The frequency of a term is the number of times it occurs in a collection of data. For example, Table 1.3 shows that 11 students ate 1 chocolate. So, the frequency of 1 chocolate is 11. Similarly, the frequency of 2 chocolates is 13.

Tally marks are made to count the number of times a term appears in a collection of data. So, tally marks tell us the frequency of a term. The following table shows how tally marks are made. Notice that | | | | and not | | | | | | | | | represents the frequency 5.

Table 1.4 Making tally marks

A frequency distribution table shows the frequencies of observations or terms. Now that we know how to represent the frequencies of observations by making tally marks, we can proceed to make a frequency distribution table for the data in Table 1.3.

Table 1.5 Frequency distribution table

The range of data is the difference between the largest observation and the smallest observation in a collection of data. For example, the range of the data in Table 1.5 = largest observation - smallest observation = 5 - 0 = 5.

Example: The number of children in the families of a village are listed below.

1 2 1 1 2 2 2 3 2 2 2 4 1 2 3 2 2 1 1 0 0 1 2 0 1 2 0 1 2 2 2 2 1. 2 3 3 4 2 1 2

Represent this as arrayed data and prepare a frequency distribution table. Also, find the range of the data.

Solution: The data in ascending order

0 0 0 0 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 4 4

The frequency distribution table for the data is as follows.

The range of data = 4 - 0 = 4.

Teacher's Note

Creating a frequency distribution table is like taking attendance in a class - you're counting how many students fall into each category to understand the overall pattern.

Graphical Representation Of Data

Showing data in the form of pictures is called graphical or pictorial representation of data. You may have seen such pictures in newspapers, magazines and on TV. They help people to get a quick understanding of numerical data. There are many ways of representing data through pictures. Some of these are pie charts, bar graphs and histograms.

Pie Graph Or Pie Chart

In a pie graph, the angles of the sectors of a circle represent the size (or frequency) of the entry. The angle is calculated by the formula:

Sectorial angle = \[\frac{\text{size of the entry}}{\text{sum of sizes of all the entries}} \times 360°\]

Example: The following table shows the number of cars of different colours in a parking space. Draw a pie graph for the data.

Solution

The total number of cars = 9 + 7 + 20 + 10 + 14 = 60.

Teacher's Note

A pie chart is like dividing a pizza among friends - each person gets a slice proportional to their share, making it easy to see who got how much at a glance.

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