Free statistics calculators designed for data scientists.
This descriptive statistics calculator:
- Calculate descriptive statistics
- Make a Histogram for the Sample
- Save & Recycle Data Between Projects
Using The Descriptive Statistics Calculator
Enter your data as a string of numbers, separated by
commas. Then hit
calculate. The descriptive statistics calculator will
generate a list of key measures and make a histogram
chart to show the sample distribution.
For easy entry, you can copy and paste your data into the
entry box from Excel. You can save your data for use with
this calculator and other calculators on this site. Just hit
the "save data" button. It will save the data in your browser
(not on our server, it remains private). Saved data sets will
appear on the list of saved datasets below the data entry panel.
To retrieve it, click the "load data" button next to it.
Interpreting Calculator Results
I usually start by examining the lovely histogram that
the calculator generates. This will show you the general
shape of the sample distribution, which will help guide
you through the balance of your analysis. In addition to
the normal distribution, other common patterns include
power-law dynamics (many low values, a few extremely
high values) and bi-modal (multi-humped). A bi-modal
distribution frequently indicates you're looking at
the combined output of two different processes or a
process that operates at multiple different states.
For example, consider the average height of the people
standing at the neighborhood bus stop after school.
Before the bus arrives, the average value is probably
around five feet. After the bus arrives - a key state
change for that process - you will have a bi-modal
distribution center around 5 feet and 3.5 feet....
Below the histogram, we provide a large list of statistics
describing the sample you entered. This includes calculating
percentiles, the interquartile range, and common statistics
for a normally distributed variable such as mean, variance,
and standard deviation. Note that we present the latter as
sample statistics (base n) and with the adjustment
for representing a population (base n-1). We also present
counting measures such as the sample mode.
More About The Descriptive Statistics Tool
This tool has three purposes:
- Calculate descriptive statistics about your sample
- Run the histogram maker to visualize the distribution
- Make it easy to retain and share your data for re-use
Let's talk about the latter for a moment. Data is retained on your browser (indefinitely, unless you clear your cache). You can
save sample data by clicking the save button and naming your dataset. The saved dataset will by listed on a menu below the calculators on the page. You can retrieve it by clicking "load data" or delete it by clicking delete. If you want to share it via email, click the
"share" button and copy the resulting link. You can paste this link in an email or web browser and retain your information. This is a good way to back up any information you've got saved in local storage. If you need to over-write a dataset, just save it again with the
exact same dataset name. You can retrieve your saved information from most of the calculator pages on our site. This is intended to
reduce the need for you to re-enter data.
This descriptive statistics is designed to provide a comprehensive source of descriptive statistics for a sample of measurements.
Simply enter your observations in the data entry box and hit calculate; the tool will do the rest, handling a battery of common
statistical tests. The results include a histogram graph so you can review the shape of the distribution. The tool calculates
basic descriptive statistics (serving as a mean, median, mode, and range calculator). The interquartile range calculator function
can also be very useful when dealing data from non-normal distributions. The tool generates common sample statistics (standard
deviation, standard error, sample variance). It also performs an adjustment to calculate population statistics for standard
deviation and sample variance.
Enter your observations as a string of numbers - separated by commas
or with a new line for each measurement. The sample mean calculator
will calculate the mean - or average - value of the data you provide.
It will also do basic house-keeping tasks such as counting observations
(useful for QA), identifying the mode, and calculating the sample median
and interquartile range (difference between 25th and 75% percentiles).
The interquartile range is particularly useful if you realize that your
underlying data isn't normally distributed - interquartile range is a
metric that remains useful for many different statistical distributions.
The histogram graph provides a good perspective on the shape, center,
and spread of your data.
The tool goes beyond serving as a mean, median, and mode calculator:
it also calculates sample variance, standard deviation, and standard error.
These are common measures of the degree of variation within a distribution.
The standard error calculator is useful when you want to understand how
close your sample is to the population mean. The standard deviation
calculator is useful when you want to understand the how much individuals
within the same sample should differ from the sample mean.
For the variance and standard deviation statistics, it is important
to know if you are looking at a sample or the entire population of
possible items. If we're looking at 10 items randomly pulled off an
assembly line and measured, that would be a sample. If we take every
child in the class and measure them, that would be the entire population.
This is important because it affects which statistical formula we
use to calculate variance and standard deviation.
We calculate sample variance, standard error, and standard deviation
by using the number of items in the sample. If we are measuring the
entire population, we reduce this by one (using n-1).
We also calculate a statistic known as the standard error, which
depicts the expected difference between the sample mean and the
real mean value of the underlying population. This differs from
the standard deviation. The standard deviation captures the degree
of scatter of the individual observations around the population mean.
But the effects of this scatter are reduced as we take more samples.
The standard error captures how far the sample means scatter around
the true mean of that population. Different samples drawn from that same population would usually have different sample means, which effectively
form a distribution of their own. This distribution can be associated
with the standard deviation in the following manner: for a given sample size, the standard error is the standard deviation divided by the square root of the sample size. As sample size grows, the sample means will group more closely around the population mean and standard error decreases.
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