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d to the nearest whole number. eight (in pounds) Frequency 135-139 12

d to the nearest whole number. eight (in pounds) Frequency 135-139 12

MATLAB: An Introduction with Applications
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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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.
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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