A news reporter in a city with several carbon-emitting power plants wanted to see whether local temperatures matched trends in global climate change. She focused on the four coldest months of the year.

The table shows local temperature data from November through February for the two consecutive cold seasons checked by the reporter.

[tex]\[
\text{Average Monthly Temperatures ( } {}^{\circ} F\text{ )}
\][/tex]

[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline
\text{Season} & \text{November} & \text{December} & \text{January} & \text{February} \\
\hline
2011-2012 & 61.1 & 51.9 & 53.6 & 56.5 \\
\hline
2012-2013 & 64.2 & 56.8 & 48.3 & 55.1 \\
\hline
\end{tabular}
\][/tex]

How did the mean temperature change between the two cold seasons? You may use the calculator.

A. went down by [tex]$1.4^{\circ}$[/tex]
B. went up by [tex]$0.3^{\circ}$[/tex]
C. went up by [tex][tex]$0.9^{\circ}$[/tex][/tex]
D. went up by [tex]$3.7^{\circ}$[/tex]



Answer :

Certainly! Let's analyze the data given for the seasonal temperatures and determine how the mean temperature changed between the two cold seasons.

1. List of temperatures for each season:
- For the 2011-2012 season: [tex]\( 61.1^\circ F, 51.9^\circ F, 53.6^\circ F, 56.5^\circ F \)[/tex]
- For the 2012-2013 season: [tex]\( 64.2^\circ F, 56.8^\circ F, 48.3^\circ F, 55.1^\circ F \)[/tex]

2. Calculate the mean temperature for each season:
- For the 2011-2012 season:
[tex]\[ \text{Mean of 2011-2012} = \frac{61.1 + 51.9 + 53.6 + 56.5}{4} = 55.775^\circ F \][/tex]

- For the 2012-2013 season:
[tex]\[ \text{Mean of 2012-2013} = \frac{64.2 + 56.8 + 48.3 + 55.1}{4} = 56.1^\circ F \][/tex]

3. Determine the change in mean temperature:
- Subtract the mean temperature of the 2011-2012 season from the mean temperature of the 2012-2013 season:
[tex]\[ \text{Change in mean temperature} = 56.1^\circ F - 55.775^\circ F = 0.325^\circ F \][/tex]

Based on the analysis:
- The mean temperature went up by approximately [tex]\( 0.3^\circ F \)[/tex].
- Therefore, the correct answer is:
- B. went up by [tex]\( 0.3^\circ \)[/tex]