Create and interpret frequency tables

Lesson

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?

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

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

$\editable{}$

2. 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?

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

A

If there are many different scores, each with low frequency

B

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

A

If there are many different scores, each with low frequency

B

Outcomes

S4-1

Plan and conduct investigations using the statistical enquiry cycle:– determining appropriate variables and data collection methods;– gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends;– comparing distributions visually;– communicating findings, using appropriate displays.