Statistics Calculator

Complete descriptive statistics — mean, median, mode, quartiles, SD, and more.

Enter Data Set

Data (8 values): 2, 4, 4, 4, 5, 5, 7, 9

Standard Deviation (s)

2.1381

Mean (Average)

5

Variance

4.5714

Median

4.5

Mode

4

Min / Max

2 / 9

Range

7

Statistics Calculator Formula & How It Works

Five-number summary: Min, Q1, Median, Q3, Max | IQR = Q3 − Q1
  • Q1 = 25th percentile (median of lower half)
  • Q2 = 50th percentile (median)
  • Q3 = 75th percentile (median of upper half)
  • IQR = interquartile range (middle 50% of data)

Descriptive statistics summarise data sets using measures of central tendency (mean, median, mode) and spread (range, SD, IQR). Box plots use the five-number summary. Outliers are typically values beyond Q1 − 1.5×IQR or Q3 + 1.5×IQR. Skewness measures asymmetry; kurtosis measures tail heaviness.

Statistics Calculator FAQs

What is the interquartile range (IQR)?

IQR = Q3 − Q1 (difference between 75th and 25th percentiles). It contains the middle 50% of data and is robust to outliers, unlike range. Used in box plots and outlier detection.

What is a normal distribution?

A symmetric bell-shaped distribution where mean = median = mode. Described by its mean (μ) and standard deviation (σ). The 68-95-99.7 rule applies. Many natural phenomena approximate normal distributions: heights, test scores, measurement errors.

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