d to the nearest whole number. eight (in pounds) Frequency 135-139 12
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:To approximate the mean of the grouped data, follow these steps. Make sure to round the result to the nearest whole number.
**Data Table:**
- **Weight (in pounds) | Frequency**
- 135-139 | 12
- 140-144 | 20
- 145-149 | 11
- 150-154 | 10
- 155-159 | 5
**Explanation:**
1. **Midpoint Calculation:**
- For each weight range, the midpoint is the average of the lower and upper bounds.
- 135-139: (135 + 139) / 2 = 137
- 140-144: (140 + 144) / 2 = 142
- 145-149: (145 + 149) / 2 = 147
- 150-154: (150 + 154) / 2 = 152
- 155-159: (155 + 159) / 2 = 157
2. **Weighted Mean Calculation:**
- Multiply each midpoint by its corresponding frequency.
- Add these values together.
- Divide by the total frequency (sum of all frequencies).
3. **Example Calculation:**
- \((137 \times 12) + (142 \times 20) + (147 \times 11) + (152 \times 10) + (157 \times 5)\)
- \(= 1644 + 2840 + 1617 + 1520 + 785 = 8406\)
- Total frequency = \(12 + 20 + 11 + 10 + 5 = 58\)
- Mean = \(\frac{8406}{58} \approx 145\)
Therefore, the approximate mean of the grouped data is 145 pounds.
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