Measures of Central Tendency and Dispersion
Mean, median and mode summarise location while variance and standard deviation summarise spread about the mean.
What is Measures of Central Tendency and Dispersion?
Mean, median and mode summarise location while variance and standard deviation summarise spread about the mean.
Key formula / rule: Variance is the mean of squared deviations from the mean.
Key points
- Compute mean, median, variance and standard deviation for a dataset.
- Compare datasets using appropriate measures of spread.
Common exam trap
Dividing by n when the sample variance requires n - 1.
Definitions
- Term
Measures of Central Tendency and Dispersion
- Meaning
Mean, median and mode summarise location while variance and standard deviation summarise spread about the mean.
- Term
Measures of Central Tendency and Dispersion — explanation
- Meaning
The mean is sensitive to outliers and the median is not, so the choice of summary is itself an analytical decision. Variance is measured in squared units, which is why the standard deviation is reported.
Learning objectives
Compute mean, median, variance and standard deviation for a dataset.
Compare datasets using appropriate measures of spread.
Formulae
- Key point
Variance is the mean of squared deviations from the mean.
- Key point
Standard deviation shares the units of the data; variance does not.
- Key point
The median is resistant to extreme values.
Prerequisites
MAT-U5-PS-T1-S1-C1
Common mistakes
Dividing by n when the sample variance requires n - 1.
Comparing standard deviations of datasets with very different means without using the coefficient of variation.
Keywords
Measures
Central
Tendency
Dispersion
Practice preview
What is the mean of the first five natural numbers?…
easy
For the dataset {2, 3, 5, 2, 7, 2, 8, 9}, what is the mode?…
easy
Find the median of the following data: 12, 15, 11, 13, 18, 11, 13, 12, 13.…
medium