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.

# Descriptive Statistics Calculator

• Statistics and Histogram Graph
• Save data sets in your browser
• Easily Share results via email

#### Descriptive Statistics

Sample has 28 observations.

Minimum:1.0000
25th Percentile: 3.0000
Sample Median: 3.5000
75th Percentile: 5.2500
Interquartile Range: 2.2500
Maximum: 26.0000

#### Sample Statistics (base n)

Sample Mode: 3.0000
Sample Mean: 5.1429
Variance: 25.6825
Standard Deviation: 5.0678
Standard Error: 0.9577

#### Population Statistics (base n-1)

Standard Deviation: 4.9765
Variance: 24.7653

### Observations

Click To Clear; enter values seperated by commas or new lines. Cut & Paste from Excel also works.

Can be comma separated or one line per data point; you can also cut and paste from Excel.

### Saved Datasets - Click to Restore

Saved in your browser; you can retrieve these and use them in other calculators on this site.

#### Sharing Results of The Histogram Maker

Need to pass an answer to a friend? It's easy to link and share the results of this calculator. Hit calculate - then simply cut and paste the url after hitting calculate - it will retain the values you enter so you can share them via email or social media.

### 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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