Numerical Data (Collecting and Displaying)
A great way to explain data is to display it in a graph. The key is knowing which type of graph can be used for the data you have collected.
Numerical data, as the name suggests, is data with numbers. So the size of your shoe is numerical, but the name of your favourite band isn't.
Sort this data into two groups: numerical data and categorical data
(nb. If data is not numerical, it will be categorical).
| Hair colour | Height | Weight |
| Favourite toy | Number of pets | Favourite colour |
| Time taken to get to school | Favourite flower | Class sizes |
| Best friend's name | Type of car owned | Number of cars owned |
| Age | Type of pets owned | Number of siblings |
When collecting data, you need to keep things organised. A good way to do this is to draw a table, often with a tally chart. A tally is a good way to keep track of when something happens. So if you wanted to organise a lot of coloured chocolates into groups, you could keep a tally of how many of each colour you count.
If I tried to sort out the chocolates in the image at the top of this page I could easily get lost and confused. So a tally like the one below would be useful to set out to keep track of things.
| Colour | Tally | Frequency |
|---|---|---|
| Red | II | |
| Yellow | III | |
| Blue | I | |
| Green | IIII |
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.
a) Complete the table
| Minutes taken | Tally | Frequency |
|---|---|---|
| $1$1 | ||
| $2$2 | ||
| $3$3 |
Think: Each mark on a tally represents one person. Remember you can easily spot groups of $5$5.
Do: Count up the number of tallies for each row. In the first row you can read the tally as $5+5+3$5+5+3. This sums to $13$13.
b) How many people took part in the survey?
Think: You need to find the total number of people represented in the table
Do: Add up all values in the Frequency column.
$13+17+12=42$13+17+12=42
c) How much time did most people take to complete the survey?
Think: If you want to know what most people did you need to look at the row with the highest frequency
Do: Find the row with the highest frequency, and look at how many minutes that relates to.
The row with the highest frequency is $2$2 minutes.
Question 2
Xanthe recorded her heartbeat in beats per minute (bpm) during her $60$60 minute workout. The results are shown in the line graph below.
a) After how many minutes was Xanthe’s heartbeat the highest?
Think: Look at the highest point of the graph. This represents when Xanthe's heartbeat was at its highest. Which time is this above?
Do: Use something with a straight edge to line up the top of the graph with the number directly below.
The highest point is above $40$40 minutes.
b) What was the the difference between Xanthe’s highest heart rate and lowest heart rate?
Think: You need to look at the difference between the highest and lowest points on the graph. You can use the y-axis like a number line to help calculate the difference.
Do: $130-65=65$130−65=65
c) When did Xanthe’s heart rate go back down to $65$65 beats per minute (bpm)?
Think: The important thing to look for here is when the heart rate goes back down - you are looking for a decrease in the heart rate, and for when the heart rate is first recorded again at $65$65 bpm.
Do: $60$60 minutes