Charts & Visual Data Modeling
Ogive Graph Formula: Cumulative Frequency %, Upper Class Boundaries & Grouped Median
Build a "Less-Than" Ogive cumulative frequency curve: plot Cumulative % against Upper Class Boundaries (starting at 0% at the first Lower Boundary) and compute the linearly interpolated Grouped Percentile / Median.
Plot Ogive vertices at UPPER class boundaries (never midpoints!) so percentiles read off exactly!
Whereas a Frequency Polygon plots bin counts at class midpoints (L_k + U_k) / 2, a "Less-Than" Ogive plots Cumulative Frequency F_k = SUM_{j<=k} f_j (or Cumulative Relative Percentage 100 * F_k / N) against each bin’s exact Upper Class Boundary U_k — anchored at (U_0 = L_1, 0%) on the horizontal axis! Why? Because only at U_k have all F_k observations in bins 1..k strictly accumulated!
Reading horizontally from any target percentile p (such as p = 0.50 for the Median or p = 0.75 for Q_3) to the straight-line Ogive segment [U_{m-1}, U_m] corresponds identically to the classical Linear Interpolation Grouped Percentile Formula: X_p = L_m + ((p * N - F_{m-1}) / f_m) * (U_m - L_m)!
| Ogive Vertex / Class | Upper Boundary U_k | Bin Count f_k | Cumulative Count F_k | Ogive Cumulative % |
|---|---|---|---|---|
| Origin Anchor (Below Bin 1) | 10 | 0 | 0 | 0.00% |
| Bin 1: [10, 20) | 20 | 12 | 12 | 24.00% |
| Bin 2: [20, 30) (Contains Median N/2 = 25) | 30 | 20 | 32 | 64.00% |
| Bin 3: [30, 40] | 40 | 18 | 50 | 100.00% |
Cumulative Relative Frequency (%) at Upper Boundary U_k
Computes 100 * SUM($C$2:C4) / SUM($C$2:$C$5) using SUMIFS on upper boundaries <= B4 so rows remain order-resilient.
=IF(OR(MIN(C2:C5) < 0, SUM(C2:C5) <= 0), "Requires Positive Total Sample N", ROUND(100 * SUMIFS(C2:C5, B2:B5, "<=" & B4) / SUM(C2:C5), 2))Linearly Interpolated Grouped Median from the Median Ogive Segment
Evaluates L_m + ((0.5 * N - F_{m-1}) / f_m) * (U_m - L_m) across Bin 2 ([A4, B4) = [20, 30), f_m = C4 = 20, prior cumulative count F_{m-1} = C2 + C3 = 12, N = 50).
=IF(OR(C4 <= 0, B4 <= A4, SUM(C2:C5) <= 0), "Invalid Median Class Parameters", ROUND(A4 + ((0.5 * SUM(C2:C5) - (C2 + C3)) / C4) * (B4 - A4), 2))Try the example
Use the original values or change them to test your understanding.