Descriptive statistics in Google Sheets

The example data

Exam scores of 20 students, in A2:A21:

61, 60, 70, 52, 66, 77, 71, 60, 85, 69, 63, 80, 73, 61, 79, 90, 53, 79, 67, 66

The full summary table

MODE.MULT returns a vertical list, so leave empty cells below it. Here four values are tied, each appearing twice. MODE would show only one of them.

What each number tells you

Centre: mean or median?

The mean (69.1) uses every value, so outliers pull it. The median (68) is the middle value and resists outliers. When they are close, as here, the data are fairly symmetric. When the mean is much higher than the median, a few large values are pulling it up (right skew), which is typical for incomes, reaction times or prices.

Spread: standard deviation and IQR

A standard deviation of 10.25 means scores typically sit about 10 points from the mean. The IQR (16.5) is the width of the middle 50% of the data and, like the median, ignores extreme values.

Standard deviation vs standard error

The standard deviation describes the spread of the data. The standard error (2.29) describes how precisely the mean is estimated, and it shrinks as n grows. Use the SD to describe your sample and the SE or a confidence interval when you talk about the mean.

Shape: skewness and kurtosis

Skewness near 0 means symmetric; positive means a longer right tail. KURT returns excess kurtosis, where 0 matches a normal distribution. A common rule of thumb treats values between −1 and +1 as roughly normal, but for a real check use a Shapiro-Wilk test.

Sample or population?

STDEV.S and VAR.S divide by n − 1 and are right for samples. STDEV.P and VAR.P divide by n and are only for a complete population. In coursework and research, you almost always want the .S versions.

Frequency table and histogram

Type the upper limit of each bin in C2:C5 (for example 60, 70, 80, 90), then in D2:

=FREQUENCY(A2:A21, C2:C5)

It returns the count per bin, plus one extra cell for values above the last limit. For a chart, select the data and choose Insert › Chart › Histogram chart.

Descriptive statistics by group

To summarise scores per group (with group names in column B), use conditional versions: =AVERAGEIF(B2:B21, "Group 1", A2:A21) and =COUNTIF(B2:B21, "Group 1"). For a median or SD per group, filter first: =STDEV.S(FILTER(A2:A21, B2:B21="Group 1")).

How to report it (APA style)

Report the mean and SD for roughly symmetric data, and the median and IQR for skewed data.

Frequently asked questions

Should I use STDEV.S or STDEV.P?

Use STDEV.S when your data are a sample from a larger population, which is almost always the case in research and coursework. Use STDEV.P only when you have every member of the population.

How do I calculate the standard error in Google Sheets?

There is no dedicated function. Use =STDEV.S(range)/SQRT(COUNT(range)).

Why does MODE return only one value?

MODE returns a single value even when several values are tied for most frequent. Use MODE.MULT to list all of them.

How do I get a quick summary without formulas?

Select a range: the bottom-right corner of Google Sheets shows the sum, and you can click it to see the average, minimum, maximum and count. For a full table, use formulas or an add-on.