Bivariate Data

New Zealand

Level 6 - NCEA Level 1

Lesson

When we learnt about sector graphs (or pie charts), we learnt that the whole pie represented the total data set and each sector represents a particular category in that data set. A divided bar graph is similar to a sector graph in that the bar represents the whole data set and the bar is divided into several segments to represent the proportional size of each category.

A bar graph can be any length but it can be helpful to think about what length may make your data easier to divide up- multiples of $5$5 or $10$10 are often good. Remember you don't want it too long or too short.

Say we had $100$100 jellybeans and we divided them up by colour. $30$30 were white, $28$28 were pink, $28$28 were orange and $14$14 were black.

Since there were $100$100 jellybeans, we may choose to make our divided bar graph $10$10cm long so we have an easy ratio where $1cm=\text{10 jellybeans}$1`c``m`=10 jellybeans.

To work out how much of the bar graph each colour represents, we want to write each colour as a fraction of the whole, then evaluate this fraction of the line. For example, $\frac{30}{100}$30100 (or $\frac{3}{10}$310) of the jellybeans are white and $\frac{3}{10}\times10=3$310×10=3. This means that $3$3cm of the $10$10cm bar graph should be given to the white jellybeans. Similarly $\frac{28}{100}\times10=2.8$28100×10=2.8, so $2.8$2.8cm should be given to both pink and orange and $1.4$1.4cm should be given to black.

We can check we've calculated everything correctly by adding up the length values:

$3+2.8+2.8+1.4=10$3+2.8+2.8+1.4=10 - so we know we've got everything correct.

The divided bar graph shows the percentage of total subscriptions that each newspaper has. The Age has $54000$54000 subscriptions.

What is $1%$1% of total subscriptions?

Find the total number of subscriptions.

On a divided bar graph that is $9$9 centimetres long, what length would be the equivalent of an angle of $90^\circ$90° on a sector graph? Evaluate to 2 decimal places.

Plan and conduct investigations using the statistical enquiry cycle: A justifying the variables and measures used B managing sources of variation, including through the use of random sampling C identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays D making informal inferences about populations from sample data E justifying findings, using displays and measures.

Investigate a given multivariate data set using the statistical enquiry cycle

Investigate bivariate numerical data using the statistical enquiry cycle