12.02 Problem solving with line plots
Are you ready?
Can you read information from a line plot?
Nadia measured the width of a number of small boxes, to the nearest inch. Her results are shown in the line plot below.
What is the most common box width that Nadia measured?
What is the width of the largest box that Nadia measured?
Learn
We can create a line plot from a data set in order to more easily understand key features of the data set, such as the most common value, and the largest and smallest values.
Once we can see these key features in a line plot, we can also make calculations involving them to solve problems relating to the data set. One particular kind of calculation we might want to make is to find the middle, or average, of a set of measurements. To find the average we first add the values together, then divide by the number of measurements.
For example, if the longest measurement in a set was $10\frac{1}{4}$1014 inches and the shortest measurement was $6\frac{3}{4}$634 inches, we could find the length that is exactly halfway in between by adding and dividing by $2$2:
| Average | $=$= | $\left(10\frac{1}{4}+6\frac{3}{4}\right)\div2$(1014+634)÷2 |
| $=$= | $17\div2$17÷2 | |
| $=$= | $8\frac{1}{2}$812 inches |
Make sure to look out for keywords like these that tell us which operation to use:
| addition | subtraction | multiplication | division |
|---|---|---|---|
| more | less | times | divide |
| add | subtract | multiply | split |
| give to | take away | product of | out of |
| plus | minus | per | evenly |
Apply
Question
A set of measurements are shown in the line plot below.
What is the largest measurement that was recorded?
One more measurement is taken, and is found to be exactly halfway between the largest and smallest measurements.
What is the size of this measurement?
Line plots are a way to represent sets of data visually, and can make it easier to see key features of the data set.
Once we have the key features we can then solve problems relating to the data set, which can involve any of the four operations.