Descriptive Statistics Calculator (Mean, Median, SD, Variance, Skewness)

When to use this test

• •You have a numeric variable and need to summarise its central tendency and spread.
• •You are exploring a new dataset and want a first look at every numeric column.
• •You need to check distribution shape — skewness, kurtosis, outliers — before running a parametric test.
• •You are writing up results and need a summary table for your report or thesis.
• •You want to spot data-quality issues like impossible values, duplicated entries or missing data.

How to use it

1. 1

   Upload or paste your data

   Drop a CSV or XLSX into the analyzer, or paste columns into the spreadsheet grid. The first row is treated as the header. Mixed numeric and categorical columns are fine — only numeric columns will be summarised.

2. 2

   Open the Descriptive category

   In the sidebar catalog, open Descriptive Statistics. Pick Summary Table to describe every numeric column at once, or Detailed Summary for a single column with a histogram and box plot.

3. 3

   Assign the variables

   Drag one or more numeric columns into the Variables slot. For a one-column detailed view, select a single column; for a comparison table, add as many columns as you want.

4. 4

   Inspect the summary table and plots

   DeepStats reports count (n), missing count, mean, median, mode, standard deviation, variance, minimum, 25th percentile (Q1), 75th percentile (Q3), maximum, interquartile range, skewness and kurtosis. A histogram and box plot are generated alongside the table.

5. 5

   Export or pivot to an inferential test

   Download the summary as CSV for inclusion in your report. If the distribution looks suitable, continue to an inferential test (t-test, ANOVA, regression) without re-uploading the data.

Example with sample data

Ten reaction-time measurements in milliseconds. Paste into the grid to reproduce the summary below.

RT_ms
245
262
258
271
249
280
255
268
260
273

The analyzer returns n = 10, mean ≈ 262.1, median = 261, SD ≈ 10.9, variance ≈ 119.2, min = 245, max = 280, Q1 ≈ 255.3, Q3 ≈ 270.3, IQR ≈ 15.0, skewness ≈ 0.03, kurtosis ≈ −1.0. Mean and median are close and skewness is near zero — the sample looks roughly symmetric, with moderate spread and no obvious outliers on the box plot.

How to interpret the results

You will see: count (n) and missing count, mean, median, mode, standard deviation and variance, minimum, maximum, range, Q1, Q3 and interquartile range, skewness and kurtosis, histogram and box plot.

Mean

The arithmetic average: sum of values divided by n. Useful for symmetric, outlier-free data. Very sensitive to extreme values — one very large observation can drag the mean far from where most data sits.

Median

The middle value when observations are sorted. Unaffected by outliers and a better description of 'typical' than the mean for skewed distributions such as income or reaction times.

Standard deviation and variance

SD is the typical distance of an observation from the mean. Variance is SD squared. DeepStats uses the sample formulas (dividing by n − 1), which is the correct estimator when your data is a sample of a larger population.

Quartiles and IQR

Q1 and Q3 are the 25th and 75th percentiles. IQR = Q3 − Q1 summarises the spread of the middle half of the data and is robust to outliers. The classical Tukey box-plot whiskers extend to 1.5 × IQR beyond Q1 and Q3; anything further is flagged as a potential outlier.

Skewness

A measure of asymmetry. Zero means perfectly symmetric. Positive skew means a long right tail (income, hospital stays). Negative skew means a long left tail. Rule of thumb: |skew| below 0.5 is roughly symmetric, 0.5–1 is moderately skewed, above 1 is highly skewed.

Kurtosis

A measure of tail heaviness. DeepStats reports excess kurtosis so zero corresponds to a normal distribution. Positive values (leptokurtic) indicate heavy tails and more outliers than normal; negative values (platykurtic) indicate lighter tails than normal.

Assumptions

• Measurement scale.Mean, SD and variance only make sense for interval or ratio data. For ordinal (ranked) data, use the median and IQR; for nominal data use counts and proportions.
• Complete or explicitly missing data.Missing cells should stay empty, not be coded as zero or −99. DeepStats reports the missing count separately so you can decide whether to impute, drop rows or collect more data.
• Appropriate summary for the distribution.For strongly skewed data, report the median and IQR rather than the mean and SD. For multimodal data, the mean is often misleading — describe each mode and the proportion of data in each.
• Independence.Summary statistics assume each observation is an independent draw. Repeated measurements or clustered data are fine to describe, but their standard errors will understate uncertainty.

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Frequently asked questions