# Introduction to Statistics | Introduction to Statistical Learning

In this page introduction to statistics we give the information about introduction to statistical learning, an introduction to statistical learning, measures of central tendency, measures of dispersion and analysis of bivariate data.

#### Introduction to Statistics

1.1 Meaning and Scope of Statistics, Primary and Secondary data.

1.2 Frequency, Frequency distribution, Qualitative and quantitative data, Discrete and Continuous variables.

1.3 Representation of frequency distribution by graphs: Histogram, Frequency polygon, Frequency curve, O give curve. Representation of Statistical data by Bar diagram and Pie chart.

1.4 Numerical examples based on 1.2, 1.3.

#### Measures of Central Tendency and Dispersion

2.1 Measures of central Tendency (Averages)

2.1.1 Meaning of averages, Requirements of good average.

2.1.2 Arithmetic mean (A.M.)

1. Arithmetic mean formula for Individual items, Arithmetic mean formula for Discrete Distribution data
2. Arithmetic mean formula for grouped data
3. Direct method formula to find Mean
4. Assumed mean formula to find Mean
5. Step deviation method to find Mean

Median

1. Find Median formula for Individual items, Median formula for Discrete Distribution data
2. Median formula for grouped data

Mode

1. Mode formula for Individual items, Mode formula for Discrete Distribution data, Mode formula for grouped data

Quartiles in statistics

Percentile in statistics

Decile in statistics

Combined mean, Relation between mean, median and mode.

2.1.3 Merits and Demerits of Mean, Median and Mode.

2.1.4 Numerical examples based on 2.1.2.

2.1.5 Determination of Median and Mode by Graph.

2.2 Measures of Dispersion (Variability):

2.2.1 Meaning of Variability, Absolute and Relative measures of dispersion.

2.2.2 Definitions of Q.D., M.D., S.D. and Variance, Combined variance and their relative measures, Coefficient of Variation (C.V.).

2.2.3 Numerical examples based on 2.2.2.

#### Analysis of Bivariate data:

3.1 Correlation:

3.1.1 Concept of Correlation, Types of correlation (Positive, Negative, Linear and Non-linear), Methods of studying correlation: Scatter diagram, Karl Pearson’s Correlation Coefficient (r) and Spearman’s Rank Correlation Coefficient (R).

3.1.2 Interpretation of r = + 1, r = -1, r = 0.

3.1.3 Numerical examples on 3.1.1and 3.1.2

3.2 Regression:

3.2.1. Concept of Regression, Definitions of regression coefficients and Equations of regression lines. Properties of regression coefficients (Statements only)

3.2.2 Numerical examples on 3.2.1

#### Sampling Techniques and Time Series Analysis:

4.1 Sampling Techniques:

4.1.1 Definitions of Sample, Population, Sampling, Sampling Method and Census method. Advantages of sampling method over census method.

4.1.2 Types of sampling: Simple Random Sampling (with and without replacement), Stratified Random Sampling, Merits and Demerits of S.R.S. and Stratified Sampling.

4.1.3 Simple examples on Stratified Sampling.

4.2 Time Series: (Analysis and Forecasting)

4.2.1 Meaning and components of Time Series

4.2.2 Methods of determination of trend by

(I) Method of Moving Averages.

(II) Method of Progressive Averages.

(III) Method of Least Squares (St. Line only)

4.2.3 Numerical examples on 4.2.2.