Kurtosis: what it means and how to read it

In the report: kurtosis — Excess kurtosis: how heavy the tails are compared with the normal distribution (0), with the sample correction as in Excel and SPSS; empty for fewer than 4 values or a column of equal values.

How to read it

0 — tails like the normal distribution; positive — more extreme values than normal; negative — flatter, with fewer extremes. A rough guide, not a test: within ±2 is close to normal by a strict rule; many authors accept |kurtosis| up to 7 (Kline).

In plain words

Two classes both have an average mark of 70. In class A almost everybody got between 65 and 75. In class B several students got 20 and several got 100. The teacher wanted to know which class has more marks far from the middle. She asked for kurtosis. Class B came out 2.0, and class A came out a little below zero. Zero means about the usual number of far-off marks. Above zero means more of them than usual, below zero means fewer. Now she can say that class B has many students far from the middle, and class A has fewer than usual.

How it is computed

n(n + 1) / ((n − 1)(n − 2)(n − 3)) · Σ ((x − x̄) / s)⁴ − 3(n − 1)² / ((n − 2)(n − 3)); with pop = TRUE: Σ ((x − x̄) / s)⁴ / n − 3

Where you see it

STATS_DESCRIPTIVE — Column-wise descriptive statistics with flexible metric selection and optional column filtering.

First quartile — The first quartile: 25% of the values are below it; computed as in SPSS, so it can differ from the Sheets QUARTILE and PERCENTILE functions.
Third quartile — The third quartile: 75% of the values are below it; computed as in SPSS, so it can differ from the Sheets QUARTILE and PERCENTILE functions.
10th percentile — The 10th percentile: 10% of the values are below it; computed as in SPSS, so it can differ from the Sheets QUARTILE and PERCENTILE functions.
90th percentile — The 90th percentile: 90% of the values are below it; computed as in SPSS, so it can differ from the Sheets QUARTILE and PERCENTILE functions.
Interquartile range — q3 − q1.

Get it in your sheet

One formula in a cell gives the whole report, Kurtosis included. ALS Stats is a free add-on for Google Sheets™.

Install ALS Stats from Google Workspace Marketplace (opens in a new tab)