1.2 Plotting and reading line graphs
Unlike bar charts which can be drawn horizontally or vertically, line graphs are almost always drawn with time along the horizontal axis.
Activity 1
Here are two line graphs representing the same data. Write down which you think is the best representation of the data and why.
Comment
It really depends on what you would llike the graph to demonstarte as to which line graph you think is better. If you are trying to show there is going to be a small drop in temperature over the two-week period, Graph A shows this more clearly. However, if you are trying to show the temperature is not really changing over the two-week period, Graph B would be better.
The only difference between these two line graphs in the scale on the verticel, temperature axis.
This ‘zigzag’ symbol is used to show there has been a break or a jump in the values on the axis.
It is important to consider the scale of the vertical axis when producing a line graph. It was once recommended that the value zero should always be included in your data presentation but, as you can see from graph B above, this does not always allow us to give a detailed representation of the trend. Current advice is to only include zero if it makes sense to do so for your data.
If the values on the axis do not start at zero, you will sometimes see the following symbol drawn on the axis:
It is important to consider the scale of the vertical axis when producing a line graph. It was once recommended that the value zero should always be included in your data presentation but, as you can see from graph B above, this does not always allow us to give a detailed representation of the trend. Current advice is to only include zero if it makes sense to do so for your data.
If the values on the axis do not start at zero, you will sometimes see the following symbol drawn on the axis:
Activity 2
Here is line graph A from Activity 1.
Use the line graph to answer the following multiple-choice questions
What is the maximum temperature, the the nearest degree Fahrenheit, forecast for the two-week period shown?
Answer options 4, 14, 55, 57, 60
What is the range in temperatures forecast in this period
Answer options 20, 14, 13, 12, 45 to 57
A good method for finding the median temperature forecast for this period can be found by reading the temperature value halfway between the 7th and 8th day of the month
Answer options true or false
Answer
57°F is the maximum temperature as represented by the highest point reached by the line on day 4. Pupils may incorrectly write 4 since this maximum occurs on day 4. Pupils may choose one of 14 or 60 as the maximum values on each axis scale but the blue graph line does not reach 60 degrees, and 14 is the 14th day of the month, not a temperature. 55 is a possible incorrect answer if pupils take the temperature reading for day 1.
The range in temperature is the difference between the highest and lowest temperature so this is the difference between the temperature on day 4 (57°F) and the temperature on day 11 (45°F) which is 12. Pupils often say the range is from the minimum to the maximum value i.e. from 45 to 57, and whilst this does describe how the data is spread, mathematically, the range is given as a single figure which represents the distance of the spread. 20 is the range of the temperatures on the vertical axis scale, not the actual temperatures that were recorded. The values 14 and 13 could have come from incorrect rounding or calculation, or from looking at the numbers on the horizontal day axis. False, the method described is not correct since the temperatures need to be ordered in size before calculating the median and here they are not ordered since the line fluctuates up and down over time. However, the method happens to give the correct value for the median in this case. If the 14 temperature values are placed in ascending order we get 45, 46, 46, 48, 48, 50, 50, 52, 52, 54, 54, 55, 55, 57 Halfway between the middle two values is 51°F which happens to correspond with the value of the line on the graph halfway between the 7th and 8th day!
2. 57 degrees Fahrenheit is the maximum temperature as represented by the highest point reached by the line 4
3. 57 degrees Fahrenheit is the maximum temperature as represented by the highest point reached by the line 4