Ogive Review Worksheet
TEKS S.4(D) • AP / High School Statistics Topic: Graphical Displays & Ogives
Standard Expectation: Compare and contrast different graphical or visual representations given the same data set.
Name: ___________________________
Date: ______________
Period: _______
Item 4 (Parallel Review) The table below contains data from a study of weekly physical activity times (in minutes) for 50 student-athletes. Construct an ogive from the data.
| Weekly Exercise
(minutes) | Number of Athletes
(Frequency) | Relative
Frequency | Cumulative
Frequency |
| --- | --- | --- | --- |
| 0 – 20 | 3 | 0.06 | 3 |
| 21 – 40 | 7 | 0.14 | 10 |
| 41 – 60 | 15 | 0.30 | 25 |
| 61 – 80 | 18 | 0.36 | 43 |
| 81 – 100 | 5 | 0.10 | 48 |
| 101 – 120 | 2 | 0.04 | 50 |
A)
0 20 40 60 80 100 Relative Frequency (%) 20.5 40.5 60.5 80.5 100.5 120.5 Homework / Exercise Time (minutes)
B)
0 5 10 15 20 Frequency 20.5 40.5 60.5 80.5 100.5 120.5 Exercise Time (minutes)
C)
0 10 20 30 40 50 Cumulative Frequency 20.5 40.5 60.5 80.5 100.5 120.5 Exercise Time (minutes)
D)
0 10 20 30 40 50 Relative Frequency (%) 20.5 40.5 60.5 80.5 100.5 120.5 Exercise Time (minutes)
Key Ogive Review Takeaways for the Exam:
- Definition: An ogive is a line graph representing cumulative frequency (or cumulative relative frequency).
- Non-Decreasing: Cumulative values accumulate, so ogives always trend upward or stay level.
- Class Boundaries: Points are plotted at upper class boundaries (20.5, 40.5, 60.5, ...) starting at 0.
- Distractors: Graphs displaying individual class peaks are frequency polygons, not ogives.
Ogive Review Key
Teacher Key & Guide TEKS S.4(D) Parallel Review Solution
Topic: Ogives & Cumulative Frequency
C
Correct Selection
Graph C correctly plots Cumulative Frequency against Upper Class Boundaries
Total Sample: n = 50
Graph Type: Ogive (Cumulative)
Step-by-Step Ogive Construction Procedure
1 Identify Boundaries
Use upper class boundaries to prevent gaps:
• Initial anchor: 0.5
• Class uppers: 20.5, 40.5, 60.5, 80.5, 100.5, 120.5
2 Map Cumulative Values
Pair each upper boundary with its cumulative frequency:
• (0.5, 0), (20.5, 3), (40.5, 10)
• (60.5, 25), (80.5, 43)
• (100.5, 48), (120.5, 50)
3 Verify Monotonic Rise
Cumulative counts can never decrease. An ogive forms a smooth or segmented S-curve rising to 100% of the sample (50).
Detailed Distractor & Option Analysis
Option A — Incorrect Distractor: Non-Cumulative Relative
Plots individual interval relative frequencies (e.g., peak at 36% then drops to 10% and 4%). Because it decreases, it is a relative frequency polygon, not an ogive.
Option B — Incorrect Distractor: Frequency Polygon
Plots raw single-interval frequencies (3, 7, 15, 18, 5, 2). It shows counts per bucket instead of accumulated totals, making it a standard frequency polygon.
Option C — Correct (Key) Accurate Ogive Display
Correctly sets the y-axis as Cumulative Frequency (0 to 50), anchors at (0.5, 0), and passes through (60.5, 25) and (120.5, 50) with steady upward accumulation.
Option D — Incorrect Distractor: Percentage Polygon
Shows percentage per category on a 0–50% scale. Drops sharply after the 61–80 min class, violating the cumulative accumulation property required of all ogives.
Graph Type Quick Comparison Matrix
| Graph Type | Y-Axis Variable | X-Axis Variable | Key Visual Feature |
|---|
| Ogive | Cumulative Freq / Rel Freq | Upper Class Boundaries | Always non-decreasing; reaches total N or 100% |
| Frequency Polygon | Frequency (Class count) | Class Midpoints / Boundaries | Rises and falls; anchors at y = 0 at both ends |
| Relative Freq Polygon | Relative Frequency (Proportion/%) | Class Midpoints / Boundaries | Rises and falls; sum of area/heights = 1.0 (100%) |
Common Student Pitfalls to Address During Review:
1. Confusing Ogives with Frequency Polygons: Remind students that an ogive never drops down after peaking.
2. Checking Axis Scale: If the y-axis reads "Relative Frequency (%)", the curve must reach 100%, not the raw count \(N=50\).
