Question

myp 5 math assignment 19a1 (scatter graph)
09/08-09/24
work on the following problems using your handout and class notes
name anisha period 1st

4 the following table shows the sales of hot drinks in a popular café each month, along with the average daily temperature for the month.

month	jan	feb	mar	apr	may	jun	jul	aug	sep	oct	nov	dec
sales ($ × 1000)	18	22	25	20	15	16	12	12	8	10	15	16

a which is the independent variable?
b draw a scatter graph to display the data.

grid for scatter graph

comment on the relationship between sales and temperature.

Explanation:

Part (a)

Step 1: Recall Independent Variable Definition

An independent variable is the one that is manipulated or is the cause, and it's not dependent on other variables in the context. Here, temperature is a natural factor (we don't assume sales cause temperature), while sales depend on temperature (hot drink sales likely change with temperature). So temperature is independent.

Step 1: Set Up Axes

• X - axis (Independent Variable): Temperature (\(^\circ\text{C}\)). Label the x - axis with values from around 0 to 20 (since temperatures are 5, 6, 12, 13, 18, 20, etc.).
• Y - axis (Dependent Variable): Sales (\(\$ \times 1000\)). Label the y - axis with values from around 0 to 30 (since sales are 7, 8, 10, 12, 14, 15, 16, 17, 18, 20, 21, 22, 25).

Step 2: Plot Data Points

For each month, plot the point \((\text{Temperature}, \text{Sales})\):

• Jan: \((6, 18)\)
• Feb: \((5, 22)\)
• Mar: \((12, 25)\)
• Apr: \((13, 20)\)
• May: \((18, 15)\)
• Jun: \((20, 16)\)
• Jul: \((21, 12)\)
• Aug: \((22, 12)\)
• Sep: \((17, 8)\)
• Oct: \((14, 10)\)
• Nov: \((10, 15)\)
• Dec: \((7, 16)\)

(Note: Since we can't draw the graph here, but the process is to mark these points on the grid with x - axis as temperature and y - axis as sales.)

Part (Comment on Relationship)

Step 1: Analyze Trend

Looking at the plotted points (or the data), as the temperature increases from lower values (like 5 - 12 \(^\circ\text{C}\)) to a peak (around 12 - 13 \(^\circ\text{C}\)), sales first increase (from Feb - Mar) and then as temperature continues to increase (above 13 \(^\circ\text{C}\)), sales generally decrease. So there is a non - linear (curved) relationship, or we can say a negative relationship after a certain point (or an initial positive then negative relationship).

Answer:

The independent variable is the average daily temperature (in \(^\circ\text{C}\)).

Part (b)