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10.04 Frequency tables and graphs

Lesson

In the world of data, we are often interested in the number of times, or frequency, that something occurs. It could be the number of road accidents caused by drink driving, the number of hot days in a year, or the number of visits to a website in a month.

In situations like these, where the same data value can occur multiple times, the data can be organised into a a frequency table

 

Categorical data example

As an example, let's say the colour of every car that passed though a given intersection was recorded over a ten minute period:

green, white, yellow, white, black, green, black, blue, blue, silver, white, black, green, blue, blue, white, black, silver, silver, red, red, red, black, white, blue, white, black, silver, silver, white, blue, white, black, yellow, blue, white, white, red, green, silver, black, white, black, white.

We can see that the same colours are occurring multiple times, so it makes sense to organise the data using a frequency table. If the data is categorical, the table can be used to create a bar chart.

 

Vehicle colour Tally Frequency
Black |||| |||| $9$9
White |||| |||| || $12$12
Blue |||| || $7$7
Green |||| $4$4
Silver |||| | $6$6
Yellow || $2$2
Red |||| $4$4

Notice that the frequency table has three columns:

  • The first column shows the subgroups within the data
  • The tally column (optional) uses tally marks to record the frequency of each subgroup 
  • The final column sums the tally marks and records the frequency as a number 

Not all frequency tables contain a tally column but it can make it easier to count the number of occurrences correctly.

The sum of the frequencies is equal to the total number of data values. In this case, the colours of $44$44 vehicles were recorded. 

 

Numerical data example

In the example below, a person who exercises most days has recorded the number of minutes they spend on daily exercise over an entire year. The data is first organised into a frequency table. We can see from the first row of the table that for $10$10 days of the year, they did $20$20 minutes of exercise per day.

Because the data is numerical, it is displayed using a special type of chart, called a histogram.

Number of minutes Frequency
$20$20 $10$10
$22$22 $15$15
$24$24 $25$25
$26$26 $18$18
$28$28 $42$42
$30$30 $50$50
$32$32 $38$38
$34$34 $26$26
$36$36 $12$12
$38$38 $10$10

While histograms will be explained more in the next topic, the essential difference is that the horizontal axis of a histogram represents a continuous numerical scale. The horizontal axis on a bar chart does not have a scale. It displays categories instead. The main visual difference between the two charts is that a histogram has no gaps between the bars. 

 

 

Practice questions

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

Below are the luggage weights of $15$15 passengers, rounded to the nearest kg.

$16,19,21,22,19,22,22,17,21,19,16,21,19,16,22$16,19,21,22,19,22,22,17,21,19,16,21,19,16,22

  1. Complete the frequency table.

    Weight in kilograms Frequency
    $16$16 $\editable{}$
    $17$17 $\editable{}$
    $18$18 $\editable{}$
    $19$19 $\editable{}$
    $20$20 $\editable{}$
    $21$21 $\editable{}$
    $22$22 $\editable{}$
  2. How many times did someone check-in luggage that weighed more than $19$19 kilograms?

  3. There is a baggage restriction of $20$20 kilograms.

    The airline charges each passenger $\$1.50$$1.50 for every kilogram in their luggage above this restriction.

    How much was charged altogether for excess baggage?

Question 3

The amount of snowfall (in centimetres) is recorded at the base of the mountain each day.

  1. To create a frequency histogram of the data, which values go on the horizontal axis?

    Number of days it snowed each amount

    A

    Amount of snowfall

    B

    Number of days it snowed each amount

    A

    Amount of snowfall

    B
  2. The snowfall recorded each day, to the nearest centimetre, is as follows:

    $6,2,0,3,2,2,3,4,2,0,3,2,3,4,6,4,3,0,5,3$6,2,0,3,2,2,3,4,2,0,3,2,3,4,6,4,3,0,5,3

    Construct a frequency histogram of the data.

    SnowfallAmount of snowfallFrequency5100123456

  3. On how many days did $3$3 centimetres of snow fall?

  4. On how many days did at least $4$4 centimetres of snow fall?

Outcomes

MS11-2

represents information in symbolic, graphical and tabular form

MS11-7

develops and carries out simple statistical processes to answer questions posed

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