Z-score
A z-score says how many standard deviations a value sits from the mean: z = (value − mean) ÷ standard deviation. With mean 50 and SD 10, a 60 has z = 1.
Select any words here to ask your Maestro about them.
Ana scored 82 in Chemistry, where the class averaged 70. Ben scored 92 in History, where it averaged 80. Who stands out more in their class?
What it's for: comparing values on different scales: a score on a hard test against one on an easy test, sales at a big store against a small one. Everything lands on the same scale: standard deviations.
How to calculate it: z = (value − mean) ÷ standard deviation. A z of 0 is the mean; a negative one is below it.
When the data is bell-shaped, each z matches a percentile. And a z beyond 3 or −3 is a good hint to look for an outlier.
Practice it in Is an extreme value an error or real data?, where you decide what to do with a value far from the mean.
How it's used
In Excel
Scores in B2:B31
- marked: =(B2-AVERAGE($B$2:$B$31))/STDEV.S($B$2:$B$31)The formula by hand.
- =STANDARDIZE(B2,AVERAGE($B$2:$B$31),STDEV.S($B$2:$B$31))The same with Excel's function.
- =ABS(C2)>3Flags values more than 3 standard deviations out: outlier candidates.
When to look closer
A salary at z = 2
1,000 salaries, lopsided
- marked: A salary with z = 2
In a bell curve, 2.3% sits above z = 2. With salaries, where a few are very high, will it be more or less?
Ask your Maestro about Z-score
It answers from the free course page closest to this word, the way it answers while you study.
You: What does "Z-score" mean, in plain words?
Your Maestro: I'll explain it with a case of yours: it sticks better than a definition. Which two numbers on different scales do you need to compare?
Asking about: Answers from the page "When should you use the mean, and when the median?"
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Related terms
- Standard deviation
Standard deviation measures how far data lands from the average: with an average of 30 and an SD of 2, most values fall from 28 to 32. In Excel: =STDEV.S.
- Mean (average)
To find the mean (the average), add up all the values and divide by how many there are: 15, 7, 8, 13 and 7 add up to 50, and 50 ÷ 5 = 10.
- Normal distribution (bell curve)
A normal distribution is the bell shape a lot of data takes: most values near the average, fewer and fewer out to the sides, evenly on both.
- Percentile (and quartiles)
A percentile is the value a given share of the data falls at or below: 90% falls at or below the 90th. Quartiles are the 25th, 50th and 75th.