Representing Discrete Data - Frequency Distributions

A store owner takes a survey of the customers that come in to try on shoes one Saturday afternoon. Trying to decide which sizes would be the best to stock, he compiles the following list:

6, 6, 6.5, 7, 8, 9, 7, 5.5, 8, 11, 7.5, 9, 9, 8.5, 9.5, 6.5, 7.5, 8, 9, 7, 8, 10, 10, 9.5, 8, 7.5

His son, preparing for the S1 A-level exam, suggests that a frequency distribution table might be an easy way for his father to analyze the results of his survey. "Poppa," he says, " why don't you count how many times someone orders each shoe size? Then, you can use statistics to figure out how many percent of each shoe you should stock!"

Together, they make a frequency distribution table:

"I understand why it would be important to figure out the frequency that each shoe size is selected, " says the store owner, " but why should I care about the cumulative frequency?"
After his son shows him the following table, the store owner begins to smile:

"It seems that 20% of people tried on sizes 9.5 and above, while the same percentage tried on size 8 alone! Yes! " says the store owner, "I will carry 20% of my stock in size 8!"

...which may actually be a bit hasty. You see, only a random sample of 25 customers were surveyed. A more prudent shopkeeper would gather a bit more data before translating his statistical analysis into a tool for real-world decision making. Furthermore, since shoe sizes 8.5 and 10.5 were tried on by 0% of customers, would it be wise for him to stock absolutely no shoes sized 8.5 or 10.5?

When conducting a statistical analysis, it is very important to collect an appropriate amount of data. Surveying every single one of his customers may be a bit impractical, but it would be very easy for the shop owner to take a better refined sample of his customers. Good sampling gathers data in a thoughtful way and considers not only the amount of data that should be collected, but also the portion of the population that should be surveyed. For instance, why should the shop keeper arbitrarily choose Saturday? What if most of his Saturday customers are children?