To find the mean of a frequency distribution, we follow these steps:

1. Determine the midpoint for each class.
2. Multiply each midpoint by the corresponding frequency.
3. Sum the products from step 2.
4. Divide the sum by the total frequency.

Let's apply this to the provided frequency distribution.

Step 1: Calculate the midpoints for each temperature range.

• 40–44: midpoint = $\frac{40 + 44}{2} = 42.0$
• 45–49: midpoint = $\frac{45 + 49}{2} = 47.0$
• 50–54: midpoint = $\frac{50 + 54}{2} = 52.0$
• 55–59: midpoint = $\frac{55 + 59}{2} = 57.0$
• 60–64: midpoint = $\frac{60 + 64}{2} = 62.0$

Step 2: Multiply each midpoint by its corresponding frequency.

• $42.0 \times 3 = 126.0$
• $47.0 \times 4 = 188.0$
• $52.0 \times 10 = 520.0$
• $57.0 \times 5 = 285.0$
• $62.0 \times 3 = 186.0$

Step 3: Sum the products.

$126.0 + 188.0 + 520.0 + 285.0 + 186.0 = 1305.0$

Step 4: Find the total frequency.

$3 + 4 + 10 + 5 + 3 = 25$

Step 5: Calculate the mean.

$\text{Mean} = \frac{1305.0}{25} = 52.2$

Thus, the mean of the frequency distribution is 52.2 degrees.

Comparison to the actual mean:

The computed mean (52.2°F) is close to the actual mean of 52.5°F, with a difference of 0.3°F.

Would you like more details or have any questions? Here are five related questions:

1. How does changing one frequency affect the mean?
2. What are the effects of wider intervals in frequency distributions?
3. How can we compute the median of this frequency distribution?
4. Can the mode be determined from the given data?
5. How do outliers influence the mean in a frequency distribution?

Tip: Always round to the same decimal precision throughout your calculations for consistency!