A cumulative frequency chart is a visual representation of data that contain plenty of information about the sample it's made from. By reading a cumulative frequency chart, it's possible to gather information about the shape of sample distribution, the median, quartiles and the inter-quartile range. Whereas an ordinary frequency chart is made by counting the number in the sample that belongs to a class interval, cumulative frequency charts add up frequencies of successive class intervals to produce a "running total".
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Pay attention to the shape of the chart. They must be S shaped. If a tail of the chart stays relatively flat and the head suddenly becomes steep, it signals a skewed distribution with most of the frequency falling in higher class intervals.
Check the y-axis to determine the cumulative frequency for each class interval. The cumulative frequency for the highest class interval must equal the sample size.
Look at the x-axis to read the variable whose frequency is charted as well as the size of class intervals. Note that frequency of successive class intervals are added, cumulatively, to preceding intervals to produce cumulative frequencies.
Find the sample median by drawing a horizontal line at half the total frequency. If cumulative frequency is measured in percentages, the median value occurs at 50 per cent. For example, in a cumulative frequency chart of student scores, the median score is better than the lower half of scores and worse than the higher half.
Draw a horizontal line at one-fourth of total frequency to find the lower quartile. Suppose 25 per cent of the students received 60 or less in a math exam. Then the lower quartile is 60.
Determine the upper quartile by drawing a line at three-fourths of total frequency. If 75% of students scored 90 or higher, then the upper quartile is 90.
Subtract the lower quartile from the upper quartile to calculate the inter-quartile range. In this example, the inter-quartile range is 90 -- 60, which equals 30. High range means that the scores are dispersed.
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