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Mathematics · pattern F, Dataset

Z score for a value against your own data.

Paste a dataset and a value of interest for its z score, percentile and tail probabilities, standardised against your own mean and deviation.

Inputs

Sample or population

Divide by n − 1 for a sample drawn from a wider population; by n only when the data is the entire population.

The formula used

z = (x − x̄) ÷ s

A z score says how many standard deviations a value sits from the mean. Converting it to a percentile assumes the data is roughly normal.

z score

1.305

z score for x = 82.00 against a mean of 71.50 and sample deviation of 8.045.

Mean
71.500
Standard deviation
8.045
Percentile
90.41%
Area beyond z
9.59%
Two-tailed p
0.1918
n
10

Your data — accent bars sit beyond one deviation

59.0085.00

Standardising makes different scales comparable.

A mark of 82 out of 100 and 61 out of 70 cannot be compared directly, but their z scores can, because each is expressed in standard deviations from its own mean. That is exactly what grading on a curve does, and why z scores appear in every standardised test.

Questions about z score

What is a good z score?
It depends on the direction wanted. For marks, +2 is roughly the 98th percentile.
Can z scores be negative?
Yes, for values below the mean. The distribution is symmetric, so −1.5 and +1.5 are equally far out.
Do I need normal data?
Not for the z score itself, which is a rescaling. Yes for converting it into a percentile.

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