Descriptive statistics calculator
Paste a column of data and get the full summary your results chapter opens with, computed the way SPSS and Excel report it.
Descriptive statistics summarise a single variable before any test is run: where the values centre, how far they spread, and what shape their distribution takes. Paste a column and this calculator returns the mean, median, standard deviation, variance, skewness, kurtosis, range, and a 95% confidence interval for the mean, using the sample conventions you will see in SPSS and Excel so the figures match your software.
Central tendency
Spread
Shape
95% confidence interval for the mean
Variance, standard deviation, skewness (G1) and excess kurtosis (G2) use the sample conventions SPSS and Excel report. A normal distribution has skewness and excess kurtosis of 0.
The conventions used here
The variance and standard deviation use the sample denominator, dividing the summed squared deviations by n - 1 rather than n:
s² = Σ(x - x̄)² / (n - 1)
Skewness is the adjusted Fisher-Pearson standardised moment (the G1 statistic SPSS and Excel report), and kurtosis is excess kurtosis (G2), so a normal distribution reads 0 on both rather than 3. The 95% confidence interval for the mean is built from the t distribution with n - 1 degrees of freedom:
x̄ ± t × (s / √n)
Because the interval uses the t distribution rather than a fixed 1.96, it widens correctly for small samples, matching the figure SPSS prints in its Explore output.
Frequently asked questions
- How do you calculate the standard deviation?
Subtract the mean from each value, square the differences, average them, and take the square root. The sample standard deviation divides by n minus one rather than n, which corrects for the bias of estimating spread from a sample. This calculator uses the sample formula, matching SPSS and the STDEV function in Excel.
- How do you interpret skewness and kurtosis scores?
Skewness measures asymmetry: a positive value means a long right tail, a negative value a long left tail, and zero a symmetric distribution. Excess kurtosis measures tail heaviness relative to the normal distribution, where positive values indicate heavier tails. Values between about -1 and +1 are generally treated as close enough to normal for most analyses.
- Is kurtosis 3 or 0?
Both conventions exist. Raw kurtosis is 3 for a normal distribution, while excess kurtosis subtracts 3 so that a normal distribution reads 0. This calculator reports excess kurtosis (G2), the version SPSS and Excel produce, so a value near zero indicates normal-shaped tails.
- What are good skewness and kurtosis values?
For data to be treated as approximately normal, skewness and excess kurtosis are commonly expected to fall between -1 and +1, though some authors accept the wider range of -2 to +2. The closer both are to zero, the more symmetric and normal-tailed the distribution. The shape figures above let you check your own data against these thresholds.