Coaching Centre
Collecting and displaying data
Categorical and numerical data, census and sample, bias in sampling, and choosing displays such as column graphs, dot plots, stem-and-leaf plots and histograms.
Types of data
Census or sample?
A census collects data from the whole population; a sample uses part of it. A sample must be random and large enough, or it may be biased.
To find how Year 8 students get to school, a student surveys only the people waiting at the bus stop. Is the sample biased?
Displays
- Categorical: column graph, pie chart.
- Small numerical sets: dot plot, stem-and-leaf plot.
- Large or continuous sets: histogram (grouped data, bars touching).
Read the stem-and-leaf plot: stem $2$ with leaves $1\ 4\ 4\ 8$. What values does it show?
Height in cm is:
It is measured, so it can take any value.
Favourite colour is:
It is a label, not a number.
Number of pets is:
It is counted.
Surveying only people at a gym about how often Australians exercise gives a sample that is:
Gym members exercise more than average.
The national census surveys:
That is what a census means.
Which display suits the heights of $200$ students?
Large continuous data is grouped in a histogram.
A stem-and-leaf plot has stem $2$, leaves $1\ 4\ 4\ 8$. What is the largest value?
Stem $2$, leaf $8$.
In a histogram, the bars:
The groups are continuous.
New numbers every time. Keep going until you get five in a row.