Chapter 12

 

CLASS IX           

(NCERT)

CHAPTER 12:                              STATISTICS

 

12.1 Introduction

• Statistics- It is a study of data.
• Data- Individual pieces of factual information used for analysis.
• Graph- Diagram of data, which makes understanding easier. It has axes. Here, we are only talking about graphs with two axes, one horizontal axis named as X axes and vertical axes as Y axes.

          As we studied earlier, data can be represented in the form of tables. Suppose we     have a data of score of 20 students in mathematics exam.

                                     Marks obtained: 10, 11, 15, 16, 20

                                     No.of students:    6, 2, 4, 5, 3

We will tabulate this as,

Mark obtained	No. of students (Frequency)
10	6
11	2
15	4
16	5
20	3

After this tabulation, we can do further calculations like mean, median, mode, etc.

                   Instead of this tabulation, we can make use of another form of representation, known as, graphical representation.

 

 

12.2 Graphical Representation of Data

                        Graphical representation of data is a mode of representing the data in the form of graphs. There are three types of data which we are going to learn in this chapter. They are.

·        Bar graphs

·        Histograms

·        Frequency polygons

Bar graphs

-         These are graphs with bars.

-         Bars are those which can be drawn vertically or horizontally.

-         It should be a closed figure.

Suppose we want to graphically represent a data, we will give the frequency, that is, no of apple trees as vertical axis and years as horizontal axis.

 

X axis	Years	2005	2006	2007	2008	2009	2010
Y axis	No of apple trees	150	225	350	150	300	375

Credits: https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/mahak-bar-graph-12-1603116043.png

Histograms

-         It is a graph that shows the frequency of numerical data using rectangles.

-         Similar to bar graphs, these also have horizontal and vertical axis.

-         These are drawn by touching the side of each rectangle.

For example, if we want to draw a histogram of patients in a hospital within an age group as shown below,

X axis (Age)	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Y axis (No of patients)	3	7	30	36	27	15	5

 

 

Credits: https://cdn1.byjus.com/wp-content/uploads/2020/06/ml-aggarwal-solutions-mathematics-class-8-chapter-19-24.png 

 

Frequency polygon

-         It is a line graph of class frequency plotted against class midpoint.

-         It is similar to histogram; the only difference is that frequency polygon contains line drawn by connecting the midpoints of the histogram bars.

Examples, to plot the frequency polygon of height of students in a class, take the height as horizontal x-axis and no of students as vertical y-axis.

x-axis (height)	140-150	150-160	160-170	170-180
y-axis (no of students)	75	162	135	25

 Plot the histogram, mark the midpoint of each bar and connect those points with a scale, as shown below.

 

Credits: https://s3-ap-southeast-1.amazonaws.com/subscriber.images/maths/2016/08/01063000/his2.png

 

 

12.3 Activities

Q.1      A family with a monthly income of ` 20,000 had planned the following    expenditures per month under various heads:

 

Heads	Expenditure (in hundred rupees)
Grocery	4
Rent	5
Education of children	5
Medicine	2
Fuel	2
Entertainment	1
Miscellaneous	1

            Draw a bar graph for the data above.

Q.2          Construct a histogram of the following data

 

Weight (in kg)	31-35	36-40	41-45	46-50	51-55	56-60
No of students	9	6	15	3	1	2

 

 

Q.3          a) Draw a frequency polygon for the above data (Q.2)

     b) Construct a histogram for Q.1 and draw the frequency polygon.