**Approximating the Mean of Grouped Data** To approximate the mean of the grouped data and round to the nearest whole number, you can follow these steps: 1. **Identify the Weight Classes and Frequency:** - Weight (in pounds): 135-139 | Frequency: 15 - Weight (in pounds): 140-144 | Frequency: 6 - Weight (in pounds): 145-149 | Frequency: 16 - Weight (in pounds): 150-154 | Frequency: 5 - Weight (in pounds): 155-159 | Frequency: 10 2. **Calculate the Midpoint for Each Weight Class:** Calculate the midpoint (\(x_i\)) of each weight class by averaging the lower and upper boundaries. - Midpoint for 135-139: \( \frac{135 + 139}{2} = 137 \) - Midpoint for 140-144: \( \frac{140 + 144}{2} = 142 \) - Midpoint for 145-149: \( \frac{145 + 149}{2} = 147 \) - Midpoint for 150-154: \( \frac{150 + 154}{2} = 152 \) - Midpoint for 155-159: \( \frac{155 + 159}{2} = 157 \) 3. **Multiply Each Midpoint by its Frequency:** - \(137 \times 15 = 2055\) - \(142 \times 6 = 852\) - \(147 \times 16 = 2352\) - \(152 \times 5 = 760\) - \(157 \times 10 = 1570\) 4. **Sum up All Frequencies and Products:** - Total of Frequencies: \(15 + 6 + 16 + 5 + 10 = 52\) - Total of Products: \(2055 + 852 + 2352 + 760 + 1570 = 7589\) 5. **Calculate the Approximate Mean:** \[ \text{Mean} = \frac{\text{Total of Products}}{\text{Total of Frequencies}} = \frac{7589}{52} \approx 146 \] Therefore, the mean
**Approximating the Mean of Grouped Data** To approximate the mean of the grouped data and round to the nearest whole number, you can follow these steps: 1. **Identify the Weight Classes and Frequency:** - Weight (in pounds): 135-139 | Frequency: 15 - Weight (in pounds): 140-144 | Frequency: 6 - Weight (in pounds): 145-149 | Frequency: 16 - Weight (in pounds): 150-154 | Frequency: 5 - Weight (in pounds): 155-159 | Frequency: 10 2. **Calculate the Midpoint for Each Weight Class:** Calculate the midpoint (\(x_i\)) of each weight class by averaging the lower and upper boundaries. - Midpoint for 135-139: \( \frac{135 + 139}{2} = 137 \) - Midpoint for 140-144: \( \frac{140 + 144}{2} = 142 \) - Midpoint for 145-149: \( \frac{145 + 149}{2} = 147 \) - Midpoint for 150-154: \( \frac{150 + 154}{2} = 152 \) - Midpoint for 155-159: \( \frac{155 + 159}{2} = 157 \) 3. **Multiply Each Midpoint by its Frequency:** - \(137 \times 15 = 2055\) - \(142 \times 6 = 852\) - \(147 \times 16 = 2352\) - \(152 \times 5 = 760\) - \(157 \times 10 = 1570\) 4. **Sum up All Frequencies and Products:** - Total of Frequencies: \(15 + 6 + 16 + 5 + 10 = 52\) - Total of Products: \(2055 + 852 + 2352 + 760 + 1570 = 7589\) 5. **Calculate the Approximate Mean:** \[ \text{Mean} = \frac{\text{Total of Products}}{\text{Total of Frequencies}} = \frac{7589}{52} \approx 146 \] Therefore, the mean
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
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![**Approximating the Mean of Grouped Data**
To approximate the mean of the grouped data and round to the nearest whole number, you can follow these steps:
1. **Identify the Weight Classes and Frequency:**
- Weight (in pounds): 135-139 | Frequency: 15
- Weight (in pounds): 140-144 | Frequency: 6
- Weight (in pounds): 145-149 | Frequency: 16
- Weight (in pounds): 150-154 | Frequency: 5
- Weight (in pounds): 155-159 | Frequency: 10
2. **Calculate the Midpoint for Each Weight Class:**
Calculate the midpoint (\(x_i\)) of each weight class by averaging the lower and upper boundaries.
- Midpoint for 135-139: \( \frac{135 + 139}{2} = 137 \)
- Midpoint for 140-144: \( \frac{140 + 144}{2} = 142 \)
- Midpoint for 145-149: \( \frac{145 + 149}{2} = 147 \)
- Midpoint for 150-154: \( \frac{150 + 154}{2} = 152 \)
- Midpoint for 155-159: \( \frac{155 + 159}{2} = 157 \)
3. **Multiply Each Midpoint by its Frequency:**
- \(137 \times 15 = 2055\)
- \(142 \times 6 = 852\)
- \(147 \times 16 = 2352\)
- \(152 \times 5 = 760\)
- \(157 \times 10 = 1570\)
4. **Sum up All Frequencies and Products:**
- Total of Frequencies: \(15 + 6 + 16 + 5 + 10 = 52\)
- Total of Products: \(2055 + 852 + 2352 + 760 + 1570 = 7589\)
5. **Calculate the Approximate Mean:**
\[
\text{Mean} = \frac{\text{Total of Products}}{\text{Total of Frequencies}} = \frac{7589}{52} \approx 146
\]
Therefore, the mean](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F508ee786-e013-45c0-a264-dadcc72c168c%2F76a3490e-417d-4307-95ca-085793f14d06%2F505o9ut.jpeg&w=3840&q=75)
Transcribed Image Text:**Approximating the Mean of Grouped Data**
To approximate the mean of the grouped data and round to the nearest whole number, you can follow these steps:
1. **Identify the Weight Classes and Frequency:**
- Weight (in pounds): 135-139 | Frequency: 15
- Weight (in pounds): 140-144 | Frequency: 6
- Weight (in pounds): 145-149 | Frequency: 16
- Weight (in pounds): 150-154 | Frequency: 5
- Weight (in pounds): 155-159 | Frequency: 10
2. **Calculate the Midpoint for Each Weight Class:**
Calculate the midpoint (\(x_i\)) of each weight class by averaging the lower and upper boundaries.
- Midpoint for 135-139: \( \frac{135 + 139}{2} = 137 \)
- Midpoint for 140-144: \( \frac{140 + 144}{2} = 142 \)
- Midpoint for 145-149: \( \frac{145 + 149}{2} = 147 \)
- Midpoint for 150-154: \( \frac{150 + 154}{2} = 152 \)
- Midpoint for 155-159: \( \frac{155 + 159}{2} = 157 \)
3. **Multiply Each Midpoint by its Frequency:**
- \(137 \times 15 = 2055\)
- \(142 \times 6 = 852\)
- \(147 \times 16 = 2352\)
- \(152 \times 5 = 760\)
- \(157 \times 10 = 1570\)
4. **Sum up All Frequencies and Products:**
- Total of Frequencies: \(15 + 6 + 16 + 5 + 10 = 52\)
- Total of Products: \(2055 + 852 + 2352 + 760 + 1570 = 7589\)
5. **Calculate the Approximate Mean:**
\[
\text{Mean} = \frac{\text{Total of Products}}{\text{Total of Frequencies}} = \frac{7589}{52} \approx 146
\]
Therefore, the mean
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