Quartiles from cumulative frequency

Let $n$ be the total frequency. The lower quartile, median and upper quartile are $Q_1$, $Q_2$ and $Q_3$. Their cumulative counts are:

The original individual values are hidden inside the grouped data, so each read from the curve is an estimate.

1. Find the required cumulative count. Use $n/4$, $n/2$ or $3n/4$ on the cumulative-frequency axis.
2. Move horizontally to the curve. The curve converts a cumulative count into an estimated value.
3. Move vertically to the value axis. Read and report the value in context. Graph readings are estimates.

For percentile $k$, enter the count axis at:

The 90th percentile is the value below which about 90% of the data lie. First calculate the count, then read from the curve exactly as you did for a quartile.

• Add frequencies down the table to obtain cumulative frequency.
• Plot each cumulative total at the upper class boundary.
• Include the lower boundary of the first class with cumulative frequency zero.
• Draw one smooth increasing curve rather than a dot-to-dot polygon.