Medians, Quartiles, and Standard Deviation

Standard Deviation

• Measures the distance from the mean.

• Represents the average distance from the mean.

• Sample Standard Deviation: \sqrt{\frac{\sum{(x_i - \bar{x})^2}}{n-1}}, where \bar{x} is the sample mean and n is the sample size.

• Population Standard Deviation: \sqrt{\frac{\sum{(x_i - \mu)^2}}{N}}, where \mu is the population mean and N is the population size.

Variance

• The square of the standard deviation

Box and Whisker Plot

• Box represents quartiles (Q1 to Q3).

• Whiskers extend to the min and max values.

• Five-Number Summary: min, Q1, median, Q3, max.

• Each section between successive numbers represents 25% of the data.

Interquartile Range (IQR)

• IQR = Q3 - Q1

• Represents the spread of the middle 50% of the data.