To calculate the correlation between the high and low temperatures for the 14 cities, we can use the formula for Pearson's correlation coefficient, which measures the strength and direction of the linear relationship between two variables:

[ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} ]

Where:

• $n$ is the number of data points (in this case, 14 cities).
• $x$ represents the high temperatures.
• $y$ represents the low temperatures.

Let me calculate this based on the given data.The Pearson correlation coefficient between the high and low temperatures for the 14 cities is approximately $0.806$. This indicates a strong positive correlation between the two variables. In other words, cities that tend to have higher high temperatures also tend to have higher low temperatures, and vice versa.

Would you like further details or have any questions?

Here are 5 related questions you could explore:

1. How do you interpret the correlation strength in statistical terms?
2. How does this correlation impact weather patterns in cities with large temperature differences?
3. Would the correlation change if we used a different set of cities or seasons?
4. How can we visually represent the correlation between high and low temperatures?
5. How would you calculate the linear regression line for this data?

Tip: When working with temperature data, be mindful of outliers that could affect correlation strength!