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📋 Statistics from a frequency table Type your frequency table (value and fᵢ) and get the mean, median, mode, range and standard deviation read from the cumulative frequency, step by step.
📝 List of data 📋 Frequency table
Data read, sorted: 0 · 0 · 0 · 0 · 1 · 1 · 1 · 1 · 1 · 1 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3
Standard deviation
√21/5 ≈ 0.92
0 2 4 6 8 fᵢ 0: 4 4 0 1: 6 6 1 2: 8 8 2 3: 2 2 3 x̄ Me Frequency table xᵢ fᵢ Fᵢ hᵢ % 0 4 4 0.2 20 % 1 6 10 0.3 30 % 2 8 18 0.4 40 % 3 2 20 0.1 10 % N 20
Mean (x̄) Add up all the data: each value times how often it appears. 0·4 + 1·6 + 2·8 + 3·2 = 28 Divide by the number of data values, N = 20: x̄ = 28 / 20 = 1.4 Median (Me) With the data sorted, the median is the middle value. There are N = 20 values, which is even. There are two middle values, in positions 10 and 11: 1 and 2. To find a position, look for the first row whose cumulative frequency (Fᵢ) reaches that number. Me = (1 + 2) / 2 = 1.5 Mode (Mo) The most repeated value is 2, 8 times: Mo = 2. Range Maximum − minimum = 3 − 0 = 3 Variance and standard deviation How far the data are from the mean, on average. For each value: its distance to the mean, squared, times its frequency. σ² = Σ fᵢ·(xᵢ − x̄)² / N = (4·(0 − 1.4)² + 6·(1 − 1.4)² + 8·(2 − 1.4)² + 2·(3 − 1.4)²) / 20 = 0.84 σ = √σ² = √21/5 ≈ 0.92 🔗 Copy link to this exercise Other statistics calculators