Ogives, Quartiles and Percentiles

Ogives, Quartiles and Percentiles

An ogive is a cumulative-frequency graph. It allows approximate reading of median, quartiles and percentiles: locate the target cumulative frequency, move horizontally to the curve, then vertically to the data axis. For grouped data, answers are estimates, so show the graph-reading method and avoid claiming false precision.

Worked reasoning

For 80 data values, $Q_1$ is at cumulative frequency 20, median at 40 and $Q_3$ at 60. Read the corresponding values from the ogive.

Exam method

1. Count total frequency N. 2. Calculate target positions $N/4,N/2,3N/4$. 3. Read across-and-down from the cumulative graph and label estimates.

Graph reading is an estimate

Use a ruler or a careful imaginary horizontal/vertical path when reading an ogive. Report a realistic precision such as 42.5 or 43 depending on graph scale; do not invent more decimal places than the axes support. The interquartile range is $Q_3-Q_1$ and describes the middle half of the data, so it is less sensitive to an extreme value than the full range. Interpret it in context: a wider IQR indicates more spread among typical observations.

One-minute retrieval: Ogives, Quartiles and Percentiles

Close the worked solution. From memory, state its central rule, name one condition that makes it valid, and reconstruct one check that would catch a typical exam error.