MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Statistical Analysis of Football Teams' Season Wins The dataset provided below represents the number of regular season wins for 10 football teams in a given season. The objective is to determine the range, mean, variance, and standard deviation of the population data set. #### Data Set: - Wins: 2, 6, 15, 4, 12, 8, 15, 8, 2, 7 #### Analysis: 1. **Range:** The range is calculated by subtracting the smallest value in the dataset from the largest value. - Formula: Range = Maximum Value - Minimum Value - In this dataset: Maximum Value = 15, Minimum Value = 2 - Calculation: Range = 15 - 2 - **Result**: The range is **13**. 2. **Mean:** The mean (average) is calculated by adding all the values together and dividing by the number of values. - Formula: Mean = (Sum of All Values) / (Number of Values) - Calculation: Mean = (2 + 6 + 15 + 4 + 12 + 8 + 15 + 8 + 2 + 7) / 10 - **Step-by-Step Summation**: - 2 + 6 = 8 - 8 + 15 = 23 - 23 + 4 = 27 - 27 + 12 = 39 - 39 + 8 = 47 - 47 + 15 = 62 - 62 + 8 = 70 - 70 + 2 = 72 - 72 + 7 = 79 - Complete Calculation: Mean = 79 / 10 - **Result**: The mean is **7.9** (to the nearest tenth). 3. **Variance and Standard Deviation:** However, the steps to calculate variance and standard deviation are not shown in the image. But for educational purposes, these values are calculated as follows: - **Variance**: Measures the spread of numbers. - Formula for Population Variance: \( \sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (X_i - \mu)^2 \) - Here, \( N \)
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Transcribed Image Text:### Statistical Analysis of Football Teams' Season Wins The dataset provided below represents the number of regular season wins for 10 football teams in a given season. The objective is to determine the range, mean, variance, and standard deviation of the population data set. #### Data Set: - Wins: 2, 6, 15, 4, 12, 8, 15, 8, 2, 7 #### Analysis: 1. **Range:** The range is calculated by subtracting the smallest value in the dataset from the largest value. - Formula: Range = Maximum Value - Minimum Value - In this dataset: Maximum Value = 15, Minimum Value = 2 - Calculation: Range = 15 - 2 - **Result**: The range is **13**. 2. **Mean:** The mean (average) is calculated by adding all the values together and dividing by the number of values. - Formula: Mean = (Sum of All Values) / (Number of Values) - Calculation: Mean = (2 + 6 + 15 + 4 + 12 + 8 + 15 + 8 + 2 + 7) / 10 - **Step-by-Step Summation**: - 2 + 6 = 8 - 8 + 15 = 23 - 23 + 4 = 27 - 27 + 12 = 39 - 39 + 8 = 47 - 47 + 15 = 62 - 62 + 8 = 70 - 70 + 2 = 72 - 72 + 7 = 79 - Complete Calculation: Mean = 79 / 10 - **Result**: The mean is **7.9** (to the nearest tenth). 3. **Variance and Standard Deviation:** However, the steps to calculate variance and standard deviation are not shown in the image. But for educational purposes, these values are calculated as follows: - **Variance**: Measures the spread of numbers. - Formula for Population Variance: \( \sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (X_i - \mu)^2 \) - Here, \( N \)
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