To effectively interpret data from a cumulative frequency graph, it is essential to identify key statistical values, such as the median, quartiles, and percentiles.

A cumulative frequency graph, commonly referred to as an ogive, provides a visual representation of how data accumulates across a specified range. In this graph, the x-axis typically represents the data values, while the y-axis indicates the cumulative frequency.

To determine the median, first locate the point where the cumulative frequency reaches half of the total frequency. From this point, draw a horizontal line to intersect the curve, and then drop a vertical line down to the x-axis. The x-coordinate at this intersection represents the median.

To find the lower quartile ($Q_1$) and the upper quartile ($Q_3$), apply the same method at 25% and 75% of the total frequency, respectively. These quartiles provide valuable insight into the spread of the middle 50% of your data set. The interquartile range (IQR), calculated as $IQR = Q_3 - Q_1$, indicates the range within which the central half of your data lies.

Percentiles can also be extracted from a cumulative frequency graph. For instance, to find the 90th percentile, identify the point that corresponds to 90% of the total frequency on the y-axis. Draw a horizontal line to the curve, and then drop a vertical line to the x-axis. The x-coordinate at this point represents the 90th percentile, indicating the value below which 90% of the data falls.

By analyzing these key statistical points, you can gain valuable insights into the distribution, central tendency, and variability of your data set.