Statistics

IB Higher Level Mathematics : Core

6. Statistics

6.1

Concept of population and sample. Discrete data and continuous data. Frequency tables.

See the Statistics Glossary for basic definitions.

6.2

Presentation of data. Grouped data; mid-interval values; interval width; upper and lower boundaries.
Frequency histograms.

SticiGui, from the University of California at Berkeley, aims to provide "Statistical Tools for Internet and Classroom Instruction with a Graphical User Interface". Included in this extensive site are a Glossary of Statistical Terms, and a complete Text. The first chapter, Tables, Percentiles, and Histograms, has explanations of such topics as frequency tables, histograms, and percentiles, median, and quartiles. The second chapter is titled Measures of Location and Spread. For basic definitions, see Presenting Data, from the Statistics Glossary. Also see Describing Univariate Data, from HyperStat Online, an introductory-level hypertext statistics book. Descriptive Statistics, from the Discovering Important Statistical Concepts Using Spreadsheets site, has a downloadable workbook containing Excel spreadsheets on mean, standard deviation, boxplots and histograms. Histograms are discussed in Continuous Random Variables and Histograms, part of Calculus and Probability for Liberal Arts and Business Majors. The Exploring Data site, from Education Queensland, contains information, worksheets, etc. on a wide variety of statistical topics, including Histograms, Boxplots, Measures of Location and Measures of Spread.

The histogram on the left matches the boxplot on the right.
See Matching Histograms and Boxplots. From the Exploring Data site.
Used with permission.

6.3

Measures of central tendency: sample mean

; median.

See Measures of Location and Spread, from SticiGui. There is a section on mean and median in Mean, Median, Variance and Standard Deviation, courtesy of Calculus Applied to Probability and Statistics for Liberal Arts and Business Majors.

See Measures of Location, from Education Queensland's Exploring Data site.

6.4

Cumulative frequency; cumulative frequency graphs; quartiles and percentiles.

See Boxplots, from Education Queensland's Exploring Data site.

A boxplot with explanations.
See Describing Univariate Data, from HyperStat Online.
Used with permission.

6.5

Measures of dispersion: range; interquartile range; sample standard deviation, s_n.
The unbiased estimate, s_n-1, of the population standard deviation s.

See Measures of Spread, from the Exploring Data site. This site also has a Measures of Spread Worksheet.
Also see Measures of Location and Spread, from SticiGui.

The answer to a student's question at the Dr. Math website discusses Measures of Dispersion.
Also, refer to the section on standard deviation at Mean, Median, Variance and Standard Deviation.