Ogive vs Cumulative Relative Frequency

Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.

Ogive (cumulative relative frequency graph)

Graphs and displays

An ogive is a cumulative relative frequency graph: each point gives the proportion of values at or below a number, so the curve rises to 1.

An ogive plots running totals instead of the count inside each bin, so it answers questions of the form how much of the data sits at or below this value. For example, with 40 test scores, if 30 of them are 80 or lower the graph passes through the point (80,0.75)(80, 0.75), since 30/40=0.7530 / 40 = 0.75. The curve never goes down and finishes at 11, that is, 100 percent, which makes it a direct way to read percentiles off a graph. The AP Statistics course framework does not name ogives, so you will meet them more often in college courses and older textbooks.

Full entry for ogive

Cumulative relative frequency

Describing data

Cumulative relative frequency is the running proportion of the data that falls at or below a given value or category.

Cumulative relative frequency tells you what fraction of the data you have accounted for by the time you reach a certain point, so it rises to 1 as you work through the ordered categories. You compute it as cumulative countn\frac{\text{cumulative count}}{n}, where nn is the total number of observations. In a class of 40 students, if 10 scored below 70 and another 14 scored in the 70s, the cumulative count through the 70s is 24 and the cumulative relative frequency is 24/40=0.6024/40 = 0.60. That 0.60 is also a statement about position: the top of the 70s band sits at roughly the 60th percentile.

Full entry for cumulative relative frequency

Where each one fits in the course