### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Relation between Mean, Median and Mode

(i) For a symmetrical distribution

Mean = Mode = Median

(ii)  For a moderately asymmetrical distributions

Mode = Median – Mean

Measure of Dsipersion:

(i) Range -:

The range is the difference between two extreme observations

i.e. Range =

Where, = Greatest observation of distribution

= Lowest observation of distribution

(ii)  Mean Deviation (M.D) -:

For a set of observations the mean deviation about an average (mean/median/mode) is given by

For a frequency distribution

(iii) Standard Deviation (S.D) -:

Standard deviation is defined as the positive square root of the arithmetic mean of the squares of the deviations of the given values from their arithmetic mean.

For frequency distribution

Standard deviation is regarded as the best measure of dispersion because it satisfies almost all the properties of an ideal measure of dispersion.

(iv) Variance -:

Square of the standard deviation is called as variance .

Root Mean Square Deviation (S):

Mean Square Deviation -:

Analysis of Frequency Distribution -:

The coefficient of variation is defined as

Where and are the standard deviation and mean of the data, respectively.

Shortcut Method to Find Variance -:

Where

Shortcut Method to Find Standard Deviation -:

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