NCERT Class 9 Maths Chapter 14 Notes - Statistics Download PDF

Class 9 Chapter 12 Statistics Notes PDF – Download Free Study Material

Careers360 brings you NCERT Class 9 Maths Chapter 12 Statistics notes, carefully prepared by subject experts to simplify your studies and help in exams. A downloadable PDF is available — click the link below to access it.

Download PDF

NCERT Class 9 Maths Chapter 12 Statistics: Notes

Statistics

A branch of mathematics concerned with data collection, analysis, interpretation and presentation is known as statistics.

Data

Any numerical or non-numerical figures, facts or other information that is collected for a particular purpose is called data.

Frequency

The number of occurrences of a particular datum is called the frequency.

Ungrouped Data

When the observation is not organised in groups, then this type of data is called ungrouped data.

Grouped Data

When the observations are organised in groups, this is called grouped data.

Class Interval

The size of the data on which the class is divided is called the class interval.

Class width = upper class limit – lower class limit

Regular and Irregular Class Interval

When the class interval is of the same size, it is called a regular class interval.
Example: 0 - 10, 10 - 20, 20 - 30, 30 - 40

When the class interval is of a different size, it is called an irregular class interval.
Example: 0 - 10, 10 - 35, 35 - 45, 45 - 60

Frequency Table

It shows the occurrence of a particular variable in a tabular form.

Sorting

Arranging data in a particular order (ascending or descending order) is called sorting data.

Ungrouped Frequency Table

A frequency table in which data is not arranged in any particular order, then is called an ungrouped frequency table.

Grouped Frequency Table

A frequency table in which data is arranged in any particular order, either in ascending or descending order then is called a grouped frequency table.

Graphical Representation of Data

Some of the graphical representations of data are as follows.

Bar Graphs

Bar graphs represent data using bars of equal width and space between them on the axis. The frequency of data is represented through the height of the bar. Bar graphs are used for discrete data intervals.
For example:

The representation of these data in a bar graph is as follows.

Histogram

Similar to the bar graph, histograms are also used for the graphical representation of data, but this is used for continuous data intervals. In this graph, the area of the rectangle or frequency represented by the height of the graph and the width is called the class intervals.

Frequency Polygon

When the midpoints of each rectangle are joined by using line segments in the histogram, this is called the frequency polygon. It can be drawn without a histogram.

Midpoint of the Class Interval

The class mark or the midpoint of the circle can be calculated as:

Class mark = $\frac{\text{(Upper limit + Lower limit)}}{2}$

A frequency polygon can be drawn using the given class mark.

Example: In a company, employees of different departments work for different numbers of months and the tabular data is shown below. Draw the histogram for the table shown below.

Class mark = $\frac{\text{(Upper limit + Lower limit)}}{2}$

Class mark = $\frac{(100 + 50)}{2}$ = 75

Similarly, determine the class mark for all values.

The histogram for the given tabular data is shown below; in this graph, ABCDEF is called the frequency polygon.

How to Use the Statistics Class 9 Notes Effectively?

Statistics become easier when we understand how data is collected and shown using graphs. This chapter primarily teaches us how to read and interpret graphs in a simple way. When we revise these ideas slowly, working with data becomes much easier. Class 9 Maths chapter 12 notes help us do that. Here are some more points on how these notes are important.

• Read the examples of bar graphs and other graphs first so we understand how data is shown.
• Practise drawing simple graphs to learn how to label axes and plot values correctly.
• Keep the NCERT Class 9 Maths chapter 12 notes with you when solving questions to check steps and avoid mistakes.
• Use the NCERT Class 9 Maths chapter 12 notes to build a strong base, because these data and graph skills help us again in higher classes and real-life maths.

Statistics Class 9 Notes: Previous Year Question and Answer

Question 1:
The mean of 20 observations was 42. It was found later that observation 54 was wrongly taken as 45. The corrected new mean is:

Solution:

The mean of 20 initial observations = 42
Sum of initial observations = 42 × 20 = 840
Wrong entry = 45
Correct entry = 54
Sum after correction = 840 – 45 + 54 = 849
$\therefore$ Final mean = $\frac{849}{20}$ = 42.45
Hence, the correct answer is 42.45.

Question 2:
The median of the following data will be _________.
32, 25, 33, 27, 35, 29, and 30

Solution:

Given numbers:
32, 25, 33, 27, 35, 29, and 30
⇒ the given data is in ascending order = 25, 27, 29, 30, 32, 33, 35
The median of this data is the middlemost number of this data (as the total number of data is odd)
So, median term = $[\frac{7 + 1}{2}]^{th}$
= $[\frac{8}{2}]^{th}$
= $4^{th}$ term
⇒ Median = 30
Hence, the correct answer is 30.

Question 3:
Find the mode for the given distribution (rounded off to two decimal places).

Solution:

Here, the maximum frequency is 11, and the corresponding class is 25–30.
So the modal class is 25–30.
Now lower limit of the modal class ($l$) = 25,
Frequency of the modal class ($f_1$) = 11
Frequency of the preceding modal class ($f_0$) = 9
Frequency of the succeeding modal class ($f_2$) = 10
class size ($h$) = 5
We know, mode = $l + (\frac{f_1-f_0}{2f_1-f_0-f_2})×h$
= $25 + (\frac{11-9}{2(11)-9-10})×5$
= $25 + (\frac{2}{3})×5$
= $25 + 3.33$
= $28.33$
Hence, the correct answer is 28.33.

NCERT Class 9 Maths Notes – Chapter-Wise Links

We at Careers360 compiled all the NCERT class 9 Maths notes in one place for easy student reference. The following links will allow you to access them.

NCERT Solutions for Class 9

Students must check the NCERT solutions for Class 9 Maths and Science given below:

• NCERT Solutions for Class 9 Maths
• NCERT Solutions for Class 9 Science

NCERT Exemplar Solutions for Class 9

Students must check the NCERT exemplar solutions for Class 9 Maths and Science given below:

• NCERT Exemplar Class 9 Maths Solutions
• NCERT Exemplar Class 9 Science Solutions

NCERT Books and Syllabus

To learn about the NCERT books and syllabus, read the following articles and get a direct link to download them.

• NCERT Books Class 9 Maths
• NCERT Syllabus Class 9 Maths
• NCERT Books Class 9
• NCERT Syllabus Class 9
• NCERT Books for Class 9 Science