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Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 56.3 degrees. Low Temperature (F) 40-44 45-49 50-54 55-59 Frequency 3 7 11 4 The mean of the frequency distribution is (Round to the nearest tenth as needed.) degrees. 60-64 1

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 56.3 degrees. Low Temperature (F) 40-44 45-49 50-54 55-59 Frequency 3 7 11 4 The mean of the frequency distribution is (Round to the nearest tenth as needed.) degrees. 60-64 1

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
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### Calculating the Mean of Data from a Frequency Distribution To find the mean of the data summarized in the given frequency distribution, follow these steps: 1. **List the Midpoints**: Calculate the midpoint for each temperature range. - Midpoint of 40-44: \( \frac{40 + 44}{2} = 42 \) - Midpoint of 45-49: \( \frac{45 + 49}{2} = 47 \) - Midpoint of 50-54: \( \frac{50 + 54}{2} = 52 \) - Midpoint of 55-59: \( \frac{55 + 59}{2} = 57 \) - Midpoint of 60-64: \( \frac{60 + 64}{2} = 62 \) 2. **Multiply Midpoints by Frequencies**: Multiply each midpoint by its corresponding frequency. - \( 42 \times 3 = 126 \) - \( 47 \times 7 = 329 \) - \( 52 \times 11 = 572 \) - \( 57 \times 4 = 228 \) - \( 62 \times 1 = 62 \) 3. **Sum All the Products**: Add all of the results from step 2. - \( 126 + 329 + 572 + 228 + 62 = 1317 \) 4. **Sum the Frequencies**: Add all of the frequencies together. - \( 3 + 7 + 11 + 4 + 1 = 26 \) 5. **Calculate the Mean**: - Mean = \( \frac{\text{Sum of Products}}{\text{Sum of Frequencies}} = \frac{1317}{26} \approx 50.7 \) Thus, the mean of the frequency distribution is approximately **50.7 degrees**. (Round to the nearest tenth as needed.) ### Comparison with the Actual Mean Compare the computed mean to the actual mean of 56.3 degrees to assess accuracy. ### Visual Representation The table listed above contains low temperatures (in °F) categorized in ranges, along with their corresponding frequencies detailing how often each temperature range occurs. | Low Temperature (°F) | 40-44 | 45-49 | 50-54 |
Transcribed Image Text:### Calculating the Mean of Data from a Frequency Distribution To find the mean of the data summarized in the given frequency distribution, follow these steps: 1. **List the Midpoints**: Calculate the midpoint for each temperature range. - Midpoint of 40-44: \( \frac{40 + 44}{2} = 42 \) - Midpoint of 45-49: \( \frac{45 + 49}{2} = 47 \) - Midpoint of 50-54: \( \frac{50 + 54}{2} = 52 \) - Midpoint of 55-59: \( \frac{55 + 59}{2} = 57 \) - Midpoint of 60-64: \( \frac{60 + 64}{2} = 62 \) 2. **Multiply Midpoints by Frequencies**: Multiply each midpoint by its corresponding frequency. - \( 42 \times 3 = 126 \) - \( 47 \times 7 = 329 \) - \( 52 \times 11 = 572 \) - \( 57 \times 4 = 228 \) - \( 62 \times 1 = 62 \) 3. **Sum All the Products**: Add all of the results from step 2. - \( 126 + 329 + 572 + 228 + 62 = 1317 \) 4. **Sum the Frequencies**: Add all of the frequencies together. - \( 3 + 7 + 11 + 4 + 1 = 26 \) 5. **Calculate the Mean**: - Mean = \( \frac{\text{Sum of Products}}{\text{Sum of Frequencies}} = \frac{1317}{26} \approx 50.7 \) Thus, the mean of the frequency distribution is approximately **50.7 degrees**. (Round to the nearest tenth as needed.) ### Comparison with the Actual Mean Compare the computed mean to the actual mean of 56.3 degrees to assess accuracy. ### Visual Representation The table listed above contains low temperatures (in °F) categorized in ranges, along with their corresponding frequencies detailing how often each temperature range occurs. | Low Temperature (°F) | 40-44 | 45-49 | 50-54 |
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