Descriptive Statistics Calculator

Descriptive statistics summarise your data before any hypothesis test: the centre (mean, median, mode), the spread (standard deviation, variance, range, IQR) and the shape (skewness and kurtosis). Paste a column of numbers to get an SPSS-style table, a histogram, a normality check based on skewness and kurtosis, and an APA sentence.

How to use this calculator

  1. Copy one column of numbers from Excel or SPSS (or type them separated by commas or spaces).
  2. Paste them into the box.
  3. Click Calculate.
  4. Use skewness, kurtosis and the histogram to judge whether the data are roughly normal before choosing a test.

Formula

Mean x̄ = Σx / n        SD = √[Σ(x − x̄)² / (n − 1)]        SE = SD / √n
Skewness G₁ = [n / ((n − 1)(n − 2))] Σ((x − x̄)/s)³
Kurtosis G₂ = [n(n + 1) / ((n − 1)(n − 2)(n − 3))] Σ((x − x̄)/s)⁴ − 3(n − 1)² / ((n − 2)(n − 3))

Step-by-step example

  1. 15 scores: 12, 15, 14, 10, 18, 20, 15, 13, 17, 16, 14, 19, 11, 15, 22.
  2. Mean = 231 / 15 = 15.40; median = 15.00; mode = 15.
  3. SD = 3.36; SE = 0.87.
  4. Skewness = 0.33, kurtosis = -0.33: close to zero, so roughly normal.

How to interpret the results

Report the mean and SD for roughly normal data, or the median and IQR for skewed data. For normality, many textbooks treat skewness between −2 and +2 and kurtosis between −7 and +7 as acceptable (Hair et al., 2010; Byrne, 2010); stricter guides use ±1. Dividing skewness or kurtosis by its standard error gives a z-score; |z| above 1.96 suggests significant non-normality, though with large samples this test is very sensitive.

How to report it in APA 7 style

Scores (N = 15) ranged from 10 to 22 (M = 15.40, SD = 3.36, Mdn = 15.00). Skewness (0.33) and kurtosis (-0.33) values were within acceptable ranges for normality.

Statistical symbols (t, F, p, r, M, SD, N, d) should be italicised in your thesis.

Assumptions

  • Numeric (interval or ratio) data; for categorical data, report frequencies and percentages instead.
  • Skewness needs at least 3 values and kurtosis at least 4; both are unstable in small samples.

How to do it in SPSS, R or Excel

SPSS: Analyze → Descriptive Statistics → Explore (or Frequencies). R: psych::describe(x). Excel: Data Analysis ToolPak → Descriptive Statistics; ScholarCalc’s skewness and kurtosis match Excel’s SKEW and KURT.

Roman Urdu mein khulasa

Descriptive statistics aap ke data ka khulasa hain: mean (average), SD (data kitna phaila hua hai) aur median (beech ki value). Skewness aur kurtosis batate hain ke data normal hai ya nahi, aur isi se faisla hota hai ke t test/ANOVA chalana hai ya non-parametric test. Aam tor par skewness ±2 aur kurtosis ±7 ke andar ho to data ko roughly normal maana jata hai.

Frequently asked questions

Should I report the mean or the median?

Report the mean and SD for roughly symmetric data. For clearly skewed data or data with outliers, report the median and interquartile range.

What skewness and kurtosis values are acceptable?

A common rule accepts skewness between −2 and +2 and kurtosis between −7 and +7 for normality; stricter sources use ±1. Also look at the histogram.

Is the kurtosis here excess kurtosis?

Yes. Like SPSS and Excel, the calculator reports excess kurtosis, so a normal distribution has a value of 0.

Why is SD calculated with n − 1?

Dividing by n − 1 gives the sample standard deviation, an unbiased estimate of the population variance. This is what SPSS, Excel’s STDEV.S and R’s sd() use.

How are quartiles calculated?

Quartiles use linear interpolation (Excel’s QUARTILE.INC and R’s default type 7). SPSS uses a slightly different method, so Q1 and Q3 may differ a little in small samples.

Can I paste Likert item responses?

Yes, but for single Likert items many researchers prefer the median and frequencies. Totals or means of multi-item scales are usually summarised with mean and SD.

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Cite this calculator

If ScholarCalc helped your analysis, you can cite it in APA 7 format:

ScholarCalc. (2026). Descriptive Statistics Calculator [Web application]. https://scholarcalc.com/descriptive-statistics-calculator/

Written and maintained by the ScholarCalc team. Last reviewed: November 2026.

Accuracy: results are computed in your browser and were validated against Python scipy, statsmodels and pingouin on test datasets. See Methodology and accuracy.