Chapter 15 Statistics Formulas 

11th-grade students looking for an 11th grade NCERT notes in Math Chapter 15, i.e. Statistics. Statistics is a very important chapter in CBSE Class 11. In this article, candidates can find the NCERT notes to Class 11 Math Chapter 15. These notes are provided by Vidyakul's top academic experts. Our experts have explained the notes step by step.

When students understand the theory behind concepts related to statistics in this chapter, they will be able to solve text questions and NCERT exercises. If you get stuck somewhere while solving these NCERT problems, see Chapter 15 "NCERT notes for 11th Grade Math" included in this article.

MATHEMATICS NOTES CHAPTER-14

Points to Remember

• Limit of the Class:

The starting and end values of each class are called the Lower and Upper limit.

• Class Interval:

The difference between upper and lower boundary of a class is called class interval or size of the class.

• Primary and Secondary Data:

The data collected by the investigator himself is known as the primary data, while the data collected by a person, other than the investigator is known as the secondary data.

• Variable or Variate: A characteristics that vary in magnitude from observation to observation. E.g., weight, height, age, etc., are variables.

• Frequency: The number of time an observation occurs in the given data, is called the frequency of the observation.

• Discrete Frequency Distribution: A frequency distribution is called a discrete frequency distribution if the data are presented in such a way that exact measurements of the units are clearly shown.

• Continuous Frequency Distribution: A frequency in which data are arranged in classes groups which are not exactly measurable.

Statistics Formulas

The formulas that are commonly used in statistical analysis are given in the table below.

Sample Mean, x¯	∑xn
Population Mean, μ	∑xN
Sample Standard Deviation, (s)	∑(x−x¯)2n−1
Population Standard Deviation, σ	σ=(x−μ)2N
Sample Variance, s2	s2=∑(xi−x¯)2n−1
Population Variance, σ2	σ2=∑(xi–μ)2N
Range, (R)	Largest data value – smallest data value

Representation of Data

There are different ways to represent data such as through graphs, charts or tables. The general representation of statistical data is:

• Bar Graph

• Pie Chart

• Line Graph

• Pictograph

• Histogram

• Frequency Distribution

	Bar Graph A Bar Graph represents grouped data with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally.
	Pie Chart A type of graph in which a circle is divided into Sectors. Each of these sectors represents a proportion of the whole.
	Line graph The line chart is represented by a series of data points connected with a straight line. The series of data points are called ‘markers.’
	Pictograph A pictorial symbol for a word or phrase, i.e. showing data with the help of pictures. As Apple, Bananas & cherries can have different numbers, and it is just a representation of data.
	Histogram A diagram is consisting of rectangles. Whose area is proportional to the frequency of a variable and whose width is equal to the class interval.
	Frequency Distribution The frequency of a data value is often represented by “f.” A frequency table is constructed by arranging collected data values in ascending order of magnitude with their corresponding frequencies.

Measures of Central Tendency

In Mathematics, statistics are used to describe the central tendencies of the grouped and ungrouped data. The three measures of central tendency are:

• Mean

• Median

• Mode

All three measures of central tendency are used to find the central value of the set of data.

Measures of Dispersion

In statistics, the dispersion measures help interpret data variability, i.e. to understand how homogenous or heterogeneous the data is. In simple words, it indicates how squeezed or scattered the variable is. However, there are two types of dispersion measures, absolute and relative. They are tabulated as below:

Absolute measures of dispersion	Relative measures of dispersion
Range Variance Standard deviation Quartiles and Quartile deviation Mean and Mean deviation	Co-efficient of Range Co-efficient of Variation Co-efficient of Standard Deviation Co-efficient of Quartile Deviation Co-efficient of Mean Deviation

Skewness in Statistics

Skewness, in statistics, is a measure of the asymmetry in a probability distribution. It measures the deviation of the curve of the normal distribution for a given set of data. 

The value of skewed distribution could be positive or negative or zero. Usually, the bell curve of normal distribution has zero skewness.

ANOVA Statistics

ANOVA Stands for Analysis of Variance. It is a collection of statistical models, used to measure the mean difference for the given set of data.

Topics and Sub-topics

Before you get into the NCERT notes for Class 11 Math Chapter 15 – Statistics, let’s go through the sections included in this chapter:

Exercise	Topics
15.1	Introduction
15.2	Measures of Dispersion
15.3	Range
15.4	Mean Deviation
15.4.1	Mean Deviation for Ungrouped Data
15.4.2	Mean Deviation for Grouped Data
15.4.3	Limitations of Mean Deviation
15.5	Variance and Standard Deviation
15.5.1	Standard Deviation
15.5.2	Standard Deviation of a Discrete Frequency Distribution
15.5.3	Standard Deviation of a Continuous Frequency Distribution
15.5.4	Shortcut method to find Variance and Standard Deviation
15.6	Analysis of Frequency Distributions
15.6.1	Comparison of two Frequency Distributions with same Mean

 

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