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Relative frequency is a concept used to describe how often a particular event occurs in relation to the total number of events. In our exercise, we apply this to payment methods at a supermarket checkout. Understanding relative frequency involves simple division. To determine the relative frequency, take the count or frequency of a specific payment method and divide it by the total number of all payment methods observed.For example, if cash was used 4 times out of 16 total transactions, the relative frequency for cash is computed as follows:\[ \text{Relative Frequency of Cash} = \frac{4}{16} = 0.25 \]Relative frequencies provide a normalized view and allow us to easily compare the occurrence of different payment methods.This is essential when we want to understand a dataset without being influenced by the size of the data.

Once we have calculated the relative frequencies, the next step is to find the percentage distribution. Percentages offer a straightforward way to interpret relative data because they fit within the familiar 0-100% scale.To convert relative frequency to percentage, simply multiply the relative frequency by 100.Continuing with our example, the relative frequency for cash is 0.25, so the percentage is calculated as:\[ \text{Percentage for Cash} = 0.25 \times 100 = 25\% \]This transformation provides a clearer picture of how each category or payment method is distributed among all transactions.Percentages are particularly useful in visual representations, like pie charts, because they allow us to quickly understand the proportion of each category in relation to the whole.

A pie chart is a circular statistical graphic divided into slices to illustrate numerical proportions. Each slice of the pie chart represents a category's percentage of the total. In our exercise, each payment method's percentage distribution will form a slice of the pie chart. The size of each slice indicates how common each payment option is among the transactions. Steps for constructing a pie chart:

• Ensure you have the percentage for each payment method.
• Draw a circle and divide it according to these percentages.
• Label each slice with the payment method and its percentage.

Pie charts are easy to interpret at a glance, making them ideal for showcasing how different categories compare within a single dataset. They can provide insights into customer preferences by visually showing which payment methods are most popular.

In any frequency distribution, categories are fundamental. They represent the different values or groups you are observing. For our payment methods exercise, categories include cash (C), check (CK), credit card (CC), debit card (D), and other (O). Every data point falls into one of these specific categories, based on the method of payment used by each customer. Each category then contributes to the frequency distribution table by tallying the number of times it appears. The choice of categories in a problem is crucial because it determines how data is grouped and analyzed. Using these categories, we can not only tally occurrences but also delve into more advanced analysis like determining relative frequencies and percentage distributions.