Σm·P(x) Calculator — Grouped Data Mean
Estimate the mean, variance, and standard deviation from a grouped frequency table. Enter the class midpoints (m) and their frequencies (f); the calculator computes x̄ = Σ m·p(x) where p(x) = f/n.
Estimated mean of the grouped frequency distribution
- 1
Total observations n
Σfᵢ = 35 - 2
Weighted sum Σ(mᵢ·fᵢ)
Σ mᵢ × fᵢ = 925 - 3
Mean x̄ = Σ(mᵢ·fᵢ) ÷ n
925 ÷ 35 = 26,4286Equivalent to Σ mᵢ·p(xᵢ) where each p(xᵢ) = fᵢ / n.
Hoe werkt deze rekenmachine?
For grouped data, the estimated mean is x̄ = Σ(mᵢ·fᵢ)/n where mᵢ is the class midpoint and n = Σfᵢ. Variance = Σ(fᵢ/n)·(mᵢ−x̄)². Enter midpoints and frequencies; this is an approximation — midpoints represent all values in a class.
Formule
How this is calculated
When data are presented in a grouped frequency table (class intervals with a count of observations per class), the individual values are unknown. The standard approach is to represent each class by its midpoint m — the average of the lower and upper class boundaries. Treating each midpoint as a discrete outcome with relative frequency p(x) = f/n (where n = Σf), the estimated mean is x̄ = Σ m·p(x) = Σ(mᵢ·fᵢ)/n.
Variance is estimated as Var(X) = Σ p(xᵢ)·(mᵢ − x̄)², the probability-weighted average of squared deviations from the mean. This is a population variance formula using the relative frequencies as weights. Standard deviation σ = √Var is in the same units as the midpoints.
This approach is an approximation — using the midpoint assumes observations are uniformly spread within each class, which may not be true. The result is the best estimate available without raw data. If individual values are available, use the descriptive-statistics or standard-deviation calculator for exact results.
Veelgestelde vragen
The midpoint of a class interval is (lower bound + upper bound) / 2. For the class 10–20, the midpoint is 15; for 20–30 it is 25, and so on. It represents the "typical" value of observations that fall in that class.
No — it is an estimate. Using the midpoint assumes observations are evenly spread within each class. The narrower the class intervals and the larger the sample, the closer the estimate is to the true mean of the raw data.
They are algebraically identical: p(x) = f/n, so Σ m·p(x) = Σ m·(f/n) = Σ(m·f)/n. The p(x) form highlights the connection to probability theory and the expected value formula E[X] = Σ x·P(x).
Ook bekend als
TG we-Calculate Editorial Team. (2026). Σm·P(x) Calculator — Grouped Data Mean [Online calculator]. TG we-Calculate. https://we-calculate.com/nl/calculator/smpx-calculator
TG we-Calculate Editorial Team. "Σm·P(x) Calculator — Grouped Data Mean." TG we-Calculate. 2026. https://we-calculate.com/nl/calculator/smpx-calculator.
TG we-Calculate Editorial Team, "Σm·P(x) Calculator — Grouped Data Mean," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/nl/calculator/smpx-calculator
@misc{wecalculate_smpx_calculator, title = {Σm·P(x) Calculator — Grouped Data Mean}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/nl/calculator/smpx-calculator}}, year = {2026}, note = {TG we-Calculate} }
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