Statistics

NZ Level 4

Create and interpret line graphs (real life)

Lesson

As we know, there are many different types of graphs that can be used to display different types of data. In this chapter, we are going to look at three types: line, step and conversion graphs. There are a couple of common features between these three types of graphs. They should have a clear heading and both axes (the horizontal and vertical lines) should be labelled.

Line graphs are very common. They are usually used to display continuous data and are often used to show changing information. Examples of data that could be displayed in a line graph include temperature, your heart rate throughout the day and a company's daily sales.

Basically, a line graph is drawn as one continuous line to show a continual (usually changing) set of scores.

The line graph shows the amount of petrol in a car’s tank.

**a)** How much petrol was initially in the tank?

**b)** What happened at $9$9am and $1$1pm?

**c)** How much petrol was used between $1$1pm and $5$5pm?

**d)** When did the petrol in the tank first fall below $18$18 litres?

Conversion graphs are line graphs which are used to convert one unit of measurement into another. We can find equivalent values between two different scales by looking at a point on the graph and comparing the values on the $x$`x`-axis (i.e. the horizontal axis) and the $y$`y`-axis (i.e. the vertical axis).

Attached is a conversion graph of Celcius to Fahrenheit.

**a)** Water freezes at $0^\circ$0°C. What is this temperature in Fahrenheit?

**b)** Would $80^\circ$80°F be above or below normal body temperature?

**c)** If the temperature increases by $1^\circ$1°C, how many degrees Fahrenheit does it increase by? Give your answer as a decimal.

$F=1.8C+\editable{}$`F`=1.8`C`+

**e)** Finally, convert $30^\circ$30°C into Fahrenheit.

Step graphs are another special type of line graph. They are used to display data which falls into separate intervals that do not overlap.

Data is displayed in steps to show the ranges . At the point where the intervals would normally overlap, an open circle is used to indicate that the graph is *discontinuous*. In other words, the open circles represent values that ARE NOT included in the range. Closed circles appears at the opposite ends of the lines to indicate values that ARE included in the range.

The graph shows the cost of sending parcels of various weight overseas.

**a)** Find the cost of sending a letter weighing $100$100 grams.

**b)** Find the cost of sending a letter weighing $300$300 grams.

**c) **What is the heaviest letter that can be sent for $\$2$$2?

Plan and conduct investigations using the statistical enquiry cycle:– determining appropriate variables and data collection methods;– gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends;– comparing distributions visually;– communicating findings, using appropriate displays.