The graph of cumulative frequency distribution is known as

Step 1: Analyze the question We are asked for the name of the graph that shows a cumulative frequency distribution.

Step 2: Explain the concept Different statistical graphs have different names:

• Histogram: bars (with no gaps) showing the frequency of each class interval.
• Frequency polygon: a line graph joining the midpoints of the tops of the histogram bars.
• Ogive (cumulative frequency curve): a graph of cumulative frequency plotted against the upper class boundaries. It is drawn as a smooth S-shaped curve, or sometimes as joined line segments.
• Relative frequency: this is a value (frequency ÷ total frequency), not a type of graph.

Step 3: Work through it Cumulative frequency means a running total of the frequencies. When we plot these running totals against the upper class boundaries and join the points, the result is an S-shaped curve called an ogive (pronounced "oh-jive").

Checking the options:

• A. Ogive: correct.
• B. Histogram: this shows ordinary frequency, not cumulative frequency.
• C. Frequency polygon: this joins midpoints of ordinary frequencies.
• D. Relative frequency: not a graph.
• E. None: wrong, because A is correct.

Step 4: Answer The graph of a cumulative frequency distribution is called an ogive, which is option A.

Exam tip: Remember "Ogive = Over-all total", meaning it builds up to the total number of observations. Also, an ogive is used to find the median, quartiles, and percentiles (for example, reading the median at the N/2 position on the cumulative frequency axis). Plot against upper class boundaries, and don't mix this up with the frequency polygon, which uses midpoints.