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$17.
Worked Examples
Question 1
In a survey some people were asked approximately how many minutes they take to decide between brands of a particular product.
Complete the frequency table.
Minutes Taken Tally Frequency 1 |||||||||||$\editable{}$ 2 ||||||||||||||$\editable{}$ 3 ||||||||||$\editable{}$ How many people took part in the survey?
What proportion of people surveyed took $1$1 minute to make a decision?
Give your answer as a fraction.
QUESTION 2
$20$20 people were asked how many hours of sleep they had gotten the previous night. The numbers below are each person’s response:
$1,6,9,8,7,9,7,10,2,3,8,7,7,3,7,3,3,7,10,9$1,6,9,8,7,9,7,10,2,3,8,7,7,3,7,3,3,7,10,9
How many people got $7$7 hours sleep?
$\editable{}$
What is the maximum amount of sleep reported by the group?
$\editable{}$
QUESTION 3
What kind of data is a frequency table more suited to represent?
If there are very few different scores, each with high frequency
AIf there are many different scores, each with low frequency
B