Math Β· Geometry & data
Statistics, Distributions, and Simple Probability
Estimated time includes reading and one quiz. Take the time you need.
Start here: key ideas
- Mean uses every value; median uses the ordered middle position.
- Mode is the most frequent value and may be absent or repeated.
- Range measures total spread from minimum to maximum.
- Outliers usually pull the mean more than the median.
- Standard deviation describes spread around the mean; compare it qualitatively.
- For equally likely outcomes, probability is favorable outcomes divided by all outcomes.
What youβll be able to do
- Calculate and interpret mean, median, mode, and range.
- Compare center and spread and explain how outliers affect summaries.
- Read distribution plots for balance, tail direction, one or two peaks, and spread; interpret standard deviation qualitatively.
- Find simple probability as favorable outcomes divided by total equally likely outcomes.
Mean uses every value; median uses the ordered middle position. Mode is the most frequent value and may be absent or repeated.
Optional review
If youβd like to review the basics, visit Tables, Charts, Graphs, and Relationships. You can start this lesson without completing those first.
Calculate center and range
The mean is sumΓ·count. The median is the ordered middle (or the mean of two middle values). The mode occurs most often and may be absent or multiple. The range is maximumβminimum.
Worked example: Sort 8,3,5,5,9 as 3,5,5,8,9. The sum is 30, so mean=6; median=5; mode=5; range=9β3=6.
Read values and how often they occur
The horizontal axis gives the number of reminders; the vertical axis gives how often each value occurs. The mode is 3 reminders because it has the highest frequency, 14. A frequency of 14 is not itself a number of reminders. The connected points are a display of whole-number categories, not fractional reminders.
Read values and how often they occur β OpenStax / Introductory Statistics, via University of HawaiΚ»i and Mathematics LibreTexts. CC BY 4.0. Source image reproduced unchanged.
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