ICSE Class 6 Maths Chapter 25 Introduction and Graphs

Unit - 6 Statistics Chapter 25

Introduction and Graphs

Introduction

Statistics is the science that deals with the collection, classification, tabulation, representation and interpretation of data.

In statistics, numerical facts are collected in the form of numbers.

If we have collected information about the heights of Class 6 children from ten different schools of Delhi, then this information in the form of numbers is called statistics.

Data

Each number collected for giving required information is called data.

Suppose information is required about the number of members in different families of a certain locality. In order to do so, a certain number of families (say, 50 families) of that locality are visited and the information so collected is summarised in the form of a table as given below:

Whatever be the method adopted, once the data is collected, it should be put in a suitable form, such that it easily gives a fair idea of the necessary information contained in the data.

In statistics data is collected and used in many ways, by government departments, educational institutions, various companies, etc.

In particular, data on population, taxes, food, education, finances, post and telegraph, agriculture, etc. is of great use. In fact, there is hardly any field today where statistical data is not used.

Representation of Data

Statistical data can be re-represented in many ways, e.g. in the form of a table (as shown above), pictures, graphs, figures, etc.

Graphs and figures have a more lasting effect on the mind compared to written statements.

In general, pictographs (pictures), bar graphs (column graphs), line graphs, pie charts, histograms, etc. are used for the representation of statistical data.

In this chapter, we shall confine our study to Bar graph, Pie graph and Line graph.

Bar Graph (Column graph)

A bar graph is the simplest form of presenting data. It consists of bars (usually vertical), all of the same width. The heights of these bars are drawn according to the number (value) they represent.

Example 1

The following table gives the birthdays of 50 children in a class:

Draw a bar graph to represent the given data.

Solution

The bar graph for the given data is as drawn below:

[Bar graph showing days of the week on horizontal axis and number of children (0-12) on vertical axis. Bars for each day with heights: Monday 7, Tuesday 10, Wednesday 6, Thursday 9, Friday 12, Saturday 4, Sunday 2]

The maximum number of children were born on Friday and the least on Sunday.

1. A bar graph may be drawn on a graph paper or on a plane paper.

2. In a bar graph, the bars are rectangles whose widths make the representation more eye catching.

3. The bars used in a bar graph may be of any suitable width, but the width of all the bars must be the same.

4. The height of a bar represents a quantity; whereas its width represents nothing.

5. The space between consecutive bars must be the same (equal).

Teacher's Note

Bar graphs are used daily in business to track sales data and compare performance across different months or products, making it easy to identify trends at a glance.

Example 2

The bar graph drawn below shows the number of tickets sold during a fair by 6 students, A, B, C, D, E and F.

[Bar graph showing students A through F on horizontal axis and number of tickets sold (0-24) on vertical axis. Bars with heights: A 16, B 9, C 20, D 7, E 24, F 14]

Using the bar graph, answer the following questions:

(i) Who sold the least number of tickets?

(ii) Who sold the maximum number of tickets?

(iii) How many tickets were sold by A, B and C taken together?

(iv) How many tickets were sold by D, E and F taken together?

(v) What is the average number of tickets sold per student?

Solution

In the given bar graph, the height of a bar gives the number of tickets sold. It is clear from the graph that:

(i) D sold the least number of tickets.

(ii) E sold the maximum number of tickets.

(iii) Number of tickets sold by A, B and C = 16 + 9 + 20 = 45.

(iv) Number of tickets sold by D, E and F = 7 + 24 + 14 = 45.

(v) Average = \(\frac{\text{Total number of tickets sold}}{\text{Total number of students}}\)

\[= \frac{16 + 9 + 20 + 7 + 24 + 14}{6} = \frac{90}{6} = 15\]

Teacher's Note

When analyzing student performance in school competitions, bar graphs help teachers quickly identify which students excelled and which need additional support, making data-driven decisions easier.

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