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Frequencies and Relative Frequencies

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In the construction of a histogram, there are several steps that we must undertake before we actually draw our graph. After setting up the classes that we will use, we assign each of our data values to one of these classes. We count the number of data values that fall into each class, and then draw the heights of the bars. These heights can be determined by two different ways that are interrelated: frequency or relative frequency.

Frequency

Frequency is an easy concept to understand. The count of how many data values fall into a certain class constitutes the frequency for this class. Classes with greater frequencies have higher bars and classes with lesser frequencies have lower bars.

Relative Frequency

Relative frequency requires one step more. Relative frequency is a measure of what proportion or percent of the data values fall into a particular class. A straightforward calculation determines the relative frequency from the frequency. All that we need to do is add up all of the frequencies. We then divide the count from each class by the sum of the frequencies.

Example

To see the difference between frequency and relative frequency we will consider the following example. Suppose we are looking at the history grades of students in 10th grade and have the classes corresponding to letter grades: A, B, C, D, F. The number of each of these grades gives us a frequency for each class:

  • 7 students with an F
  • 9 students with a D
  • 18 students with a C
  • 12 students with a B
  • 4 students with an A
To determine the relative frequency for each class we first add the total number of data points: 7 + 9 + 18 + 12 + 4 = 50. Next we divide each frequency by this sum 50.
  • 0.14 = 14% students with an F
  • 0.18 = 18% students with a D
  • 0.36 = 36% students with a C
  • 0.24 = 24% students with a B
  • 0.08 = 8% students with an A

Histograms

Either frequencies or relative frequencies can be used for a histogram. Although the numbers along the vertical axis will be different, the overall shape of the histogram will remain unchanged. This is because the heights relative to each other are the same whether we are using frequencies or relative frequencies.

Relative frequency histograms are important because the heights can be interpreted as probabilities. These probability histograms provide a graphical display of a probability distribution.

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