Maharashtra Board Class 9 Maths Part I Chapter 7 Statistics PDF Download

Statistics

Let's Recall

In earlier standards, we have learnt how to draw a simple bar-diagram and a joint bar-diagram. Also, we have observed various graphs from newspapers, magazines, television etc. and gathered information from them.

It is very important to decide according to the nature of the data, what diagram or graph would be suitable to represent it.

A farmer has produced Wheat and Jowar in his field. The following joint bar diagram shows the production of Wheat and Jowar. From the given diagram answer the following questions.

(i) Which crop production has increased consistently in 3 years?

(ii) By how many quintals the production of Jowar has reduced in 2012 as compared to 2011?

(iii) What is the difference between the production of Wheat in 2010 and 2012?

(iv) Complete the following table using this diagram.

Let's Study

Sub-divided bar-diagram

Percentage bar-diagram

Primary and secondary data

Grouped and ungrouped frequency distribution

Cumulative frequency distribution

Mean, Median and Mode for ungrouped data

Teacher's Note

Bar diagrams help us see information quickly. In India, we use bar diagrams to show crop production in different years and compare which crop is better.

Exam Trick

Remember: Bar diagram = picture of numbers. Just like we draw pictures, we draw bars to show numbers. Taller bar means more number.

Points to Remember

Bar diagrams show information using bars or rectangles.

We can compare two things using bar diagrams.

The height of the bar shows the amount or number.

We need a scale to draw correct bar diagrams.

Let's Learn

Sub-Divided Bar Diagram

To compare the information in the given data, we can also draw another type of bar-diagram.

To draw it, we add the numerical values of the entities, decide a scale and show the total by a bar proportional to the scale. Then we divide the bar in parts, proportional to the entities we had added. Hence this type of diagram is called a sub-divided bar diagram.

Now let us show the information in the previous example by a sub-divided bar diagram.

(i) Show the total production of the year 2010 by a bar. The height of the bar should be to the decided scale.

(ii) Show the production of wheat by lower part of the bar, the height of which is to the scale.

(iii) Obviously, remaining part of the bar denotes the production of Jowar for the year.

(iv) Similarly draw divided bars to show productions of the years 2011 and 2012.

When two quantities are compared using percentages, it is more informative. We have studied this before. For example, if there is Rs.600 profit on Rs.2,000 and Rs.510 profit on Rs.1,500; Rs.600 looks greater amount. But if we calculate their percentages they are 30% and 34% respectively. Hence it is clear that Rs.510 profit on Rs.1,500 is a more profitable transaction.

Teacher's Note

Percentages help us compare things fairly. In India, we use percentages to compare student scores across different classes or years.

Exam Trick

Remember: Percentage = part out of 100. Like 30% means 30 out of 100. It helps us compare unequal things equally.

Points to Remember

Percentages always add up to 100.

We can compare things better using percentages.

Percentage = (part / whole) × 100.

Sub-divided bar diagrams show parts of a whole.

Percentage Bar Diagram

To compare the given information in a different way, it is converted into percentages and then a sub-divided bar diagram is drawn. Such diagram is known as Percentage bar-diagram.

The information in the previous example is converted into percentages as shown in the adjacent table.

The information is shown in the percentage bar diagram by following steps.

(i) Yearly productions of Wheat and Jowar are converted into percentages.

(ii) The height of each bar to scale is taken as 100.

(iii) The percentage of production of Wheat is shown by the lower part of the bar to the scale.

(iv) The remaining upper part of the bar shows percentage production of Jowar.

Information of more than two entities can be shown by a sub divided bar diagram or by a percentage bar diagram.

Teacher's Note

Percentage bar diagrams show parts of 100. In a Indian family, we use this to show how much money we spend on food, clothes, and other things.

Exam Trick

Remember: Percentage bar = always 100. Divide 100 into parts like 30%, 20%, 50%. All parts together make 100%.

Points to Remember

Percentage bars always total 100 percent.

Each part shows a percentage of the total.

Different colors show different parts.

We can compare parts of different wholes using percentages.

Solved Examples

Example 1

In the neighbouring figure, percentage bar-diagram is given. Percentage expenses on different items of two families are given. Answer the following questions based on it.

(i) Write the percentage expenses of every component for each family.

(ii) Which family spends more percent of expenses on food as compared to the other and by how much?

(iii) What are the percentage expenses on other items?

(iv) Which family shows more percentage expenses on electricity?

(v) Which family's percentage expense is more on education?

Solution

(ii) Food expenses of family A are more by 10% as compared with family B.

(iii) Other expenses of family A are 15% and that of family B are 10%.

(iv) Percentage expenses on electricity of family B is greater.

(v) Percentage expenses on education are more of family B.

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