Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 

52.552.5 

degrees.

Low Temperature 

​(circle◦​F)

40minus−44

45minus−49

50minus−54

55minus−59

60minus−64
 
Frequency

33

44

1010

55

33

Question content area bottom

Part 1

The mean of the frequency distribution is 

enter your response here 

degrees. 

​(Round to the nearest tenth as​ needed.)

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.

| Temperature Range (°F) | Midpoint (x) | Frequency (f) |
|------------------------|--------------|---------------|
| 40–44                  | 42.0         | 3             |
| 45–49                  | 47.0         | 4             |
| 50–54                  | 52.0         | 10            |
| 55–59                  | 57.0         | 5             |
| 60–64                  | 62.0         | 3             |

### 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!

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 52.5 degrees.
Low Temperature (°F): 40-44, 45-49, 50-54, 55-59, 60-64
Frequency: 3, 4, 10, 5, 3

Learn how to calculate the mean of a frequency distribution using temperature data. This example demonstrates the process of finding midpoints, calculating weighted sums, and determining the mean. Suitable for high school students (Grades 9-12). The computed mean is 52.2°F, compared to the actual mean of 52.5°F.

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