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Frequency Tables


Frequency refers to how often an event occurs. We often construct frequency tables as an easy way to display data because we can have one column as a list showing the possible outcomes that may occur, a second column with tally marks of the frequency of each event (although this column isn't always included), and a third with the total frequency as a number.  Frequency tables are useful for surveys, as you can keep a running total easily each time someone responds.

When we're collecting data, a score may occur more than once. So, rather than cross out a number and rewrite the new frequency each time, we can use a tally system. Each time a score occurs, we draw a line like so:

When a score occurs for the fifth time, we draw a line through the other four like this:

This just makes it easy to count when we finish recording results. For example, in the picture below, there are $3$3 groups of $5$5 and $2$2 extra lines. What would the total frequency be in this case?

Well, $3\times5+2=17$3×5+2=17, so the total frequency in this case is $17$17.


Worked Examples

Question 1

In a survey some people were asked approximately how many minutes they take to decide between brands of a particular product.

  1. Complete the frequency table.

    Minutes Taken Tally Frequency
    1 |||| |||| ||| $\editable{}$
    2 |||| |||| |||| || $\editable{}$
    3 |||| |||| || $\editable{}$
  2. How many people took part in the survey?

  3. What proportion of people surveyed took $1$1 minute to make a decision?

    Give your answer as a fraction.


$20$20 people were asked how many hours of sleep they had gotten the previous night. The numbers below are each person’s response:


  1. How many people got $7$7 hours sleep?


  2. What is the maximum amount of sleep reported by the group?



What kind of data is a frequency table more suited to represent?

  1. If there are very few different scores, each with high frequency


    If there are many different scores, each with low frequency



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