Measures of Dispersion Lab

STA-169 · Semester II · Statistics I

beginner25 minAvailable

Measures of Dispersion

Spread matters — two datasets can share a mean yet differ wildly.

Data

56616366687070727578

Dot plot (mean = 67.9)

Measurements

Range56 - 78

Variance (s²)43.88

Std deviation (s)6.62

Q1 / Q363 / 72

IQR9.0

Std deviation is in the same units as the data — that's why it's preferred over variance for reporting. IQR is robust to outliers, range is not.

Lab brief

Objective

Compare range, variance, standard deviation and IQR across two datasets and see how outliers and sample size affect each measure.

Theory & concepts

Spread matters as much as center. Range reacts to a single extreme value, the standard deviation reacts to every value but is unit-bearing, the IQR ignores the tails, and the coefficient of variation makes spread comparable across different units. This lab pits all four against datasets you can edit.

Rendering diagram…

Measuring how spread out values are

Prerequisites

Lesson: Measures of dispersion
Lesson: Coefficient of variation

Instructions

1Enter two datasets with the same mean but different spreads.
2Record range, variance, sd, IQR and CV for both.
3Add an outlier to one dataset and note which measures jump and which hold steady.
4Compare CV between datasets that use different units (e.g. cm vs kg).

Tasks

Same mean, different spread
Build two datasets with equal means but clearly different standard deviations.
Outlier sensitivity
Show which of the four measures is most and least affected by one outlier.
Relative comparison
Use CV to compare spread across two different measurement units.

Self-check

Standard deviations computed match hand calculations.
The student correctly identifies IQR as the most outlier-robust measure shown.
CV is used correctly to compare datasets in different units.

Environment

editable datasetslive variance and sdIQR highlightcoefficient of variation

Measures of Dispersion Lab · Statistics I · Learn CSIT