Week 2 BEA140 Summarising and presenting data

Mean

The arithmetic average, calculated by adding all observations and dividing by the number of observations.

Median

The middle value after the data has been sorted from smallest to largest.

Mode

The value that occurs most frequently in a dataset.

Skewness

The shape of a distribution where extreme values pull the mean away from the median.

Right-skewed distribution

A distribution where a few large values pull the mean upward, so Mode < Median < Mean.

Left-skewed distribution

A distribution where a few small values pull the mean downward, so Mean < Median < Mode.

Variance

A measure of spread that calculates the average squared distance of observations from the mean.

Standard deviation

The square root of variance, showing how spread out observations are in the original units of the data.

Z-score

A standard score showing how many standard deviations an observation lies from the mean.

Empirical rule

For bell-shaped data, about 68% of observations fall within 1 standard deviation, 95% within 2, and 99.7% within 3.

Interquartile range (IQR)

A measure of spread calculated as Q3 - Q1, showing the range of the middle 50% of observations.

Outlier rule

A rule that identifies possible high outliers as values above Q3 + 1.5 × IQR.