Grouped Data Mean Calculator

For grouped data, the mean is computed using class midpoints as representative values. Each class midpoint is multiplied by its frequency, then divided by the total frequency.

• L_i, U_i are lower and upper class limits.
• m_i is the class midpoint.
• f_i is the class frequency.

1. Select Class intervals or Midpoints input.
2. Choose Table or Paste mode for entry.
3. Fill rows with valid numbers and positive frequencies.
4. Set decimal places and optionally enable strict checks.
5. Click Calculate mean to see results above.
6. Use the result buttons to download CSV or PDF.

This table shows typical class intervals with frequencies.

Grouped means summarize continuous data when raw observations are unavailable. Each class is represented by its midpoint m, so the estimate reflects the center of mass of the grouped distribution. If your bins are 0–10, 10–20, and so on, the calculator converts each bin to a single value (5, 15, …) and weights it by frequency. This approach is common in survey tabulations, exam score bands, and sensor readings stored as ranges. Keep units consistent.

You can enter class intervals or provide midpoints directly. Interval mode requires lower and upper limits, and it computes m = (L + U)/2 automatically. Midpoint mode is useful when your source already reports centers. Frequencies must be positive; decimals are allowed for weighted samples. Strict checks highlight overlaps or out‑of‑order bins and warn when class widths differ, which can complicate comparisons across datasets. Paste mode accepts comma, tab, or spaced values, so you can copy rows from spreadsheets quickly. Example interval row: 20, 30, 12.

For every row, the calculator computes f·m and accumulates Σf and Σ(f·m). The final mean is x̄ = Σ(f·m)/Σf, shown with 0–10 decimal places. When “Show computation table” is enabled, you get a transparent audit trail: limits, midpoints, frequencies, row products, and totals. This is ideal for classroom demonstrations, peer review, and reproducible analytics notes. Example: if Σf = 36 and Σ(f·m) = 820, then x̄ = 22.7778.

Because midpoints approximate within‑class values, the maximum per‑observation deviation from the midpoint is half the class width (w/2). With wider bins, the grouped mean can drift from the raw mean, especially for skewed classes. Reduce error by using narrower, consistent widths, or by aligning bin edges with natural breakpoints. Always report the binning scheme alongside the mean when publishing results.

After calculation, export a CSV that mirrors the computation table for spreadsheets and pipelines. The PDF export produces a ready‑to‑share report with the mean, totals, and the formula used. These downloads support quick handoffs to stakeholders, attachments for lab notebooks, and inclusion in documentation. For best practice, keep the exported files with your dataset version and analysis date.