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QUESTION 2

A statistician at the weather bureau presented the average Gauteng temperature for a given year, which was predicted using old time series data. His prediction outlines a clear picture of what to expect in the future. However, the data includes only sunny days and locations above an altitude of 1530 m.

Table 1: Monthly Average Temperatures in Gauteng Province

\begin{tabular}{|c|c|c|}
\hline
\begin{tabular}{c}
Months of the \\
Year
\end{tabular} & Night (°C) & Day (°C) \\
\hline January & 17.5 & 28.6 \\
\hline February & 17.3 & 26.8 \\
\hline March & 15.9 & 27.3 \\
\hline April & 12.5 & 24.5 \\
\hline May & 8.5 & 21.8 \\
\hline June & 5.5 & 20.1 \\
\hline July & 5.2 & 21.1 \\
\hline August & 8.2 & 23.4 \\
\hline September & 12.1 & 27.6 \\
\hline October & 14.6 & 26.3 \\
\hline November & 16.0 & 27.5 \\
\hline December & 17.1 & 28.4 \\
\hline
\end{tabular}

Which graphical display can best display the given data? Show the graphical display.



Answer :

GinnyAnswer
To visually represent the monthly average temperatures in Gauteng province, a line graph would be the most suitable graphical display. This is because line graphs effectively show trends over time, making it easy to compare night and day temperatures across different months of the year.

Let's discuss in detail how to plot the data and display the graphical representation:

### Steps to Create the Graphical Display:

1. Identify Data:
- Months: January, February, March, April, May, June, July, August, September, October, November, December.
- Night Temperatures: 17.5°C, 17.3°C, 15.9°C, 12.5°C, 8.5°C, 5.5°C, 5.2°C, 8.2°C, 12.1°C, 14.6°C, 16°C, 17.1°C.
- Day Temperatures: 28.6°C, 26.8°C, 27.3°C, 24.5°C, 21.8°C, 20.1°C, 21.1°C, 23.4°C, 27.6°C, 26.3°C, 27.5°C, 28.4°C.

2. Plot the Graph:
- Create a line graph with the months on the x-axis and temperature on the y-axis.
- Plot two lines: one for night temperatures and one for day temperatures.
- Use different colors or markers to distinguish between the night and day temperature lines.

### Graphical Display:

Below is a textual representation of what the graph would typically look like.

```
Monthly Average Temperatures in Gauteng Province
|
30|
29| |
28| | |
27| | | |
26| | | |
25| | | | | |
24| | | | | |
23| | | | | |
22| | | | |
21| | | | | |
20| | | | | |
19| | | | | |
18| | | | | |
17| | | | |
16| | | | |
15| | | | | | |
14| | | | | |
13| | | | | | |
12| | | | |
11| | | | | | |
10| | | | | | |
9| | | | | | |
8| | | | |
7| | | | | | |
6| | | | | | |
5| | | | | |
----------------------------------
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

(°C)

Night Temperatures: (Green Line with bullets)
Day Temperatures: | (Blue Line with bullets)

Legend:
* Green for Night Temperatures
| Blue for Day Temperatures
```

### Description of the Graph:

- The x-axis represents the months of the year.
- The y-axis represents the temperatures in degrees Celsius (°C).
- The green line with bullets shows the average night temperatures for each month.
- The blue line with bullets shows the average day temperatures for each month.
- The legend helps differentiate between the night and day temperature lines.

This graphical display makes it easy to observe the trends in night and day temperatures over the course of the year in Gauteng province, highlighting temperature fluctuations and seasonal variations.

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