Stastics Class 11 CBSE Maths Chapter 15

Class 11 CBSE Maths Syllabus
Chapter 1:Sets
Chapter 2: Relations and Functions
Chapter 3: Trigonometric Functions
Chapter 4: Principles of Mathematical Induction
Chapter 5: Complex Numbers and Quadratic Equations
Chapter 6: Linear Inequalities
Chapter 7: Permutations and Combinations
Chapter 8: Binomial Theorem
Chapter 9: Sequences and Series
Chapter 10: Straight lines
Chapter 11: Conic Sections
Chapter 12: Introduction to 3D
Chapter 13: Limits and Derivatives
Chapter 14: Mathematical Reasoning
Chapter 15: Stastics
Chapter 16: Probability

Introduction

Mean deviation is the arithmetic mean of the absolute values of deviations about some point.
Standard deviation is the positive square root of variance.
Variance is the arithmetic mean of the squares of deviation about mean.
The distribution having a greater coefficient of variation has more variability around the central value, than the distribution having a smaller value of coefficient of variation.
Some of the important points to remember from this exercise are as follows:
- V. = σ / x̅ where x̅ ≠ 0, σ is standard deviation and x̅ is mean.
- Range = Maximum Value – Minimum Value
- Quartile deviation=Q3−Q1/2
- Variance = (Standard deviation)2= σ2
- Var(X₁ + X₂ +……+ X_n) = Var(X₁) + Var(X₂) +……..+Var(X_n)
- The variance is mostly represented as σ², s², or Var(X).
- Variance for ungrouped data: σ² = ∑(x_i – x̅)²/ n
- Variance for grouped data: σ² = ∑f_i(x_i – x̅)²/ N
- We determine the coefficient of variance for each series in order to compare the variability or dispersion of two series.
- A series is said to be more variable than another if its C.V. is higher.
- According to some, the series with a lower C.V. is more reliable than the other.
- Before we dive into the detailed solutions of the exercise, let us have a quick summary of the Miscellaneous Exercise in Chapter 15 for Class 11.
  Measure of Dispersion
  Dispersion is the measure of variations in the values of the variable. It measures the degree of scatteredness of the observation in the distribution around the central value.
  Range
  The measure of dispersion is easy to understand and easy to calculate in the range.
  The range is defined as the difference between two extreme observations of the distribution.
  Range of distribution = Largest observation – Smallest observation.
  Mean Deviation
  Mean deviation for ungrouped data.
  For n number of observations x₁, x₂, x₃,…, x_n, the mean deviation about their mean x¯ is given by
  (formulas need to be added)
  The mean deviation about their median M is as follows
  (formulas need to be added)
  Mean Deviation for Discrete Frequency Distribution
  Let the given data consist of discrete observations x₁, x₂, x₃,……., x_n occurring with frequencies f₁, f₂, f₃,……., f_n respectively
  The mean deviation about their Median M is given as
  Mean Deviation for Continuous Frequency Distribution
  
  The xi is the mid-points of the classes, and x¯ and M are respectively, the mean and median of the distribution.
  Variance
  Variance is the arithmetic mean of the square of the deviation about mean x¯.
  Let x₁, x₂, ……x_n be the n observations with x¯ as the mean, then the variance denoted by σ², is given by
  Standard Deviation
  If σ² is the variance, then σ is called the standard deviation is given by:
  The standard deviation of a discrete frequency distribution is given by:
  The standard deviation of a continuous frequency distribution is given by:
  Coefficient of Variation
  To compare two or more frequency distributions, compare their coefficient of variations. The coefficient of variation is defined as follows: