Which average should you use?
The mean uses every value, which makes it precise and also fragile — a single outlier drags it. The median is the middle value once sorted, so it ignores how extreme the extremes are; that is why incomes and house prices are always reported as medians. The mode is the most frequent value, and it is the only one that works on categories rather than numbers.
When mean and median disagree noticeably, the data is skewed, and which one you quote becomes an editorial decision worth making deliberately.
Quartiles and the IQR
Q1 and Q3 are the values a quarter and three quarters of the way through the sorted data. The gap between them — the interquartile range — contains the middle half, and is the spread measure that outliers cannot inflate. The common rule of thumb flags anything more than 1.5×IQR beyond Q1 or Q3 as an outlier worth investigating.
Quartiles here use linear interpolation, matching Excel's PERCENTILE.INC and most statistics packages.
Frequently asked questions
Can a data set have more than one mode?
Yes. Two values tied for most frequent make it bimodal, and all of them are shown. If every value appears exactly once there is no mode at all, which is reported rather than fudged.
Can I rely on this for coursework or research?
Checked against textbook examples, including the cases with more than one mode. With an even count there are two middle values, and the median is their average — a convention worth confirming.
Is my data uploaded?
No. The list stays in the page; nothing about it is sent anywhere.
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