VIPSolutionsmake table of fi*xi also and solve step by step with defination of mean as like in cheggFind the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 56.4 degrees. Low Temperature (oF) | 40-44 45-49 50-54 55-50 60-64 o Frequency 3 7 3 7 3 Ee ‘The mean of the frequency distribution is [| degrees.
Question:
make table of fi*xi also and solve step by step with defination of mean as like in chegg
Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to
the actual mean of 56.4 degrees.
Low Temperature (oF) | 40-44 45-49 50-54 55-50 60-64 o
Frequency 3 7 3 7 3
Ee
‘The mean of the frequency distribution is [| degrees.
This is AI generated Response.
Asked by: nayan
Created at: 2025-09-14 16:42:04
Asked by: nayan
Created at: 2025-09-14 16:42:04
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## Step-by-Step Solution
### **Definition of Mean for a Frequency Distribution**
The **mean** (average) of a frequency distribution is calculated using the formula:
\[
\bar{x} = \frac{\sum (f_i \cdot x_i)}{\sum f_i}
\]
Where:
- \( f_i \) = frequency of the \(i\)-th class
- \( x_i \) = midpoint of the \(i\)-th class
---
### **Step 1: Find the Class Midpoints (\(x_i\))**
| Class Interval | Midpoint (\(x_i\)) |
|----------------|--------------------|
| 40 - 44 | \( \frac{40+44}{2} = 42 \) |
| 45 - 49 | \( \frac{45+49}{2} = 47 \) |
| 50 - 54 | \( \frac{50+54}{2} = 52 \) |
| 55 - 59 | \( \frac{55+59}{2} = 57 \) |
| 60 - 64 | \( \frac{60+64}{2} = 62 \) |
---
### **Step 2: Make the Table of \(f_i\), \(x_i\), and \(f_i \cdot x_i\)**
| Class Interval | Frequency (\(f_i\)) | Midpoint (\(x_i\)) | \(f_i \cdot x_i\) |
|----------------|---------------------|--------------------|-------------------|
| 40 - 44 | 3 | 42 | 126 |
| 45 - 49 | 7 | 47 | 329 |
| 50 - 54 | 13 | 52 | 676 |
| 55 - 59 | 7 | 57 | 399 |
| 60 - 64 | 3 | 62 | 186 |
| **Total** | **33** | | **1716** |
---
### **Step 3: Calculate the Mean**
\[
\bar{x} = \frac{\sum (f_i \cdot x_i)}{\sum f_i} = \frac{1716}{33} \approx 52.0
\]
---
### **Step 4: Compare to the Actual Mean**
- **Computed Mean:** 52.0 degrees
- **Actual Mean:** 56.4 degrees
**Conclusion:**
The computed mean (52.0 degrees) is less than the actual mean (56.4 degrees).
---
## **Final Answer**
> The mean of the frequency distribution is **52.0 degrees**.
>
> The computed mean is less than the actual mean of 56.4 degrees.
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