Statistical Techniques Using R - I
Mean, Median, Mode
Mean
The average of a data set
Median
The middle value when data is ordered
If n is odd, median is the middle number, if n is even, it is the average of the two middle value
Mode
The Most frequently occurring value in a data set.
Relationship
Empirical relation: Mode = 3 x Median - 2 x Mean
Grouped Data
Mean
Where fi is the frequency and xi is the midpoint of the class intervals.
Range & Measure of Dispersion
Range
Range = Max -Min
Standard Deviation (SD)
Measure dispersion from the mean
Variance
Inclusive vs Exclusive Classes
Inclusive Class
Upper and lower class boundaries are included.
Exclusive Class
Upper class boundary is excluded.
Conversion Between Them
Inclusive to Exclusive: Subtract a small value (e.g., 0.5) from upper boundary
Exclusive to Inclusive: Add a small (e.g., 0.5) value to upper boundary
Coefficient Of Variation (CV)
Measures the relative variability
Graphical Representations
Histogram
A bar graph of frequencies for class intervals.
Bar Graph
Represents categorical data using bars.
Ogive Curve
Cumulative frequency curve.
Less Than & More Than Ogive
Represents cumulative frequency distribution for data less than or more than specific values.
Measure Of Dispersion
Quartile Deviation
Interquartile Range (IQR)
Skewness
Symmetrical Distribution
Mean = Median = Mode
Positive Skewness
Tail on the right side (Mean > Median > Mode)
Negative Skewness
Tail on the left side (Mean < Median < Mode)
Karl Pearson's Coefficient of Skewness
Bowley's Measure of Skewness
Kurtosis
Measures the "tailedness" of the distribution
Leptokurtic
Sharp peak, heavier tails
Platykurtic
Flat peak, lighter tails
Mesokurtic
Normal distribution curve
Bivariate Data
Correlation
Positive Correlation
Both variables increases together
Negative Correlation
One variable increases while the other decreases
No Correlation
No relationship between variables
Covariance
Coefficient of Correlation
Measures the strength of linear relationship between two variables
Linear Regression
Describes the relationship between dependent and independent variables
Regression Equation
