COMP3260Data Science Foundations

Module 3 · Unit 7 · 9 tutorials · Week 6

Descriptive Statistics

Mean, median, mode, variance, standard deviation and percentiles. The numbers that summarise a dataset before you plot it.

Start t-01 Module overview

Overview

Descriptive statistics answer two questions about a variable: where is its centre, and how spread out is it around that centre? Every subsequent analysis builds on these numbers, and choosing the wrong one — using a mean on a skewed variable, say — will mislead you and anyone reading your work.

This unit introduces each measure, explains when it is appropriate, and shows how the choice of measure interacts with the shape of the distribution.

Learning outcomes

By the end of this unit you will be able to

  • Compute and interpret measures of central tendency.
  • Choose between mean, median and mode for a given variable.
  • Compute and interpret variance and standard deviation.
  • Use percentiles and quartiles to describe spread.
  • Characterise the shape of a distribution from its summary statistics.

Lesson sequence

t-01

Descriptive Statistics Overview

What descriptive statistics are for and where they fit in analysis.

 t-02

Mean

The arithmetic mean and its sensitivity to extreme values.

 t-03

Median and Mode

Robust measures of centre and the modal value of a distribution.

 t-04

Variance

Measuring spread as the average squared deviation from the mean.

 t-05

Standard Deviation

Variance brought back into the units of the original variable.

 t-06

Percentiles and Quartiles

Position-based measures of spread and the five-number summary.

 t-07

Distribution Shapes

Skew, kurtosis and what the shape tells you about the data.

 t-08

Practical Lab

Computing and interpreting summary statistics on real data.

 t-09

Unit Summary

Consolidated key points and a forward look to Unit 8.

Key concepts

Mean
The arithmetic average of a set of values. Sensitive to extreme observations.
Median
The middle value when values are ordered. Robust to extreme observations.
Variance
The average squared distance of values from the mean, measuring spread in squared units.
Standard deviation
The square root of the variance, expressing spread in the same units as the original data.
Percentile
The value below which a given percentage of observations fall.

Assessment alignment

Foundation for Assignments 3 and 4

Assignment 3 (Exploratory Data Analysis) requires you to describe variables before interpreting them. Assignment 4 (Statistical Analysis) builds directly on these summaries as the input to inference.

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