Section 2.1 Graphical Summaries for Qualitative Data 37 Table 2.2 Frequency Distribution for Computer Sales Type of Computer Tally Frequency Desktop 11 Laptop 23 Notebook 9 Tablet 7 It’s a good idea to perform a check by adding the frequencies, to be sure that they add up to the total number of observations. In Table 2.2, the frequencies add up to 50, as they should. CAUTION When constructing a frequency distribution, be sure to check that the sum of all the frequencies is equal to the total number of observations. Relative frequency distributions A frequency distribution tells us exactly how many observations are in each category. Sometimes we are interested in the proportion of observations in each category. The proportion of observations in a category is called the relative frequency of the category. DEFINITION The relative frequency of a category is the frequency of the category divided by the sum of all the frequencies. Relative frequency = Frequency Sum of all frequencies Explain It Again Difference between frequency and relative frequency: The frequency of a category is the number of items in the category. The relative frequency is the proportion of items in the category. We can add a column of relative frequencies to the frequency distribution. The resulting table is called a relative frequency distribution. DEFINITION A relative frequency distribution is a table that presents the relative frequency of each category. Often the frequency is presented as well. EXAMPLE 2.2 Constructing a relative frequency distribution Construct a relative frequency distribution for the data in Table 2.2. Solution We compute the relative frequencies for each type of computer in Table 2.2 by using the following steps. Step 1: Find the total number of observations by summing the frequencies. Sum of frequencies = 11 + 23 + 9 + 7 = 50 Step 2: Find the relative frequency for the first category, desktop computers. Relative frequency for desktop = 11 50 = 0.22 Step 3: Find the relative frequencies for the remaining categories. Relative frequency for laptop = 23 50 = 0.46 Relative frequency for notebook = 9 50 = 0.18 Relative frequency for tablet = 7 50 = 0.14 Table 2.3 on page 38 presents a relative frequency distribution for the data in Table 2.2.
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