Interpret Divided Bar Graphs

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. 

Constructing a Divided Bar Graph

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}$1cm=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.

Worked Examples

Question 1

Question 2

Question 3