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For each of the given the data sets below, calculate the mean, variance, and standard deviation. (a) 2, 82, 47, 44, 72, 47, 70, 5, 37 mean = (b) 58, 51, 59, 48, 46, 45 mean = (c) 3.4, 4.2, 4.5, 2.9, 4.7 mean = variance = variance = variance = standard deviation = standard deviation standard deviation -

For each of the given the data sets below, calculate the mean, variance, and standard deviation. (a) 2, 82, 47, 44, 72, 47, 70, 5, 37 mean = (b) 58, 51, 59, 48, 46, 45 mean = (c) 3.4, 4.2, 4.5, 2.9, 4.7 mean = variance = variance = variance = standard deviation = standard deviation standard deviation -

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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### Calculating Mean, Variance, and Standard Deviation For each of the given data sets below, calculate the mean, variance, and standard deviation. --- #### Data Set (a): **Data**: 2, 82, 47, 44, 72, 47, 70, 5, 37 **Calculations**: - **Mean**: __________ - **Variance**: __________ - **Standard Deviation**: __________ --- #### Data Set (b): **Data**: 58, 51, 59, 48, 46, 45 **Calculations**: - **Mean**: __________ - **Variance**: __________ - **Standard Deviation**: __________ --- #### Data Set (c): **Data**: 3.4, 4.2, 4.5, 2.9, 4.7 **Calculations**: - **Mean**: __________ - **Variance**: __________ - **Standard Deviation**: __________ --- ### Explanation - **Mean**: The average of the data set. - **Variance**: The measure of how much the data points are spread out from the mean. - **Standard Deviation**: The square root of the variance, indicating how much the data points typically deviate from the mean. To find these values, use the following formulas: 1. **Mean** \(\mu\) = \(\frac{\sum_{i=1}^{n} x_i}{n}\) 2. **Variance** \(\sigma^2\) = \(\frac{\sum_{i=1}^{n} (x_i - \mu)^2}{n}\) 3. **Standard Deviation** \(\sigma\) = \(\sqrt{\sigma^2}\) Where \(x_i\) represents each data point and \(n\) represents the number of data points in the set.
Transcribed Image Text:### Calculating Mean, Variance, and Standard Deviation For each of the given data sets below, calculate the mean, variance, and standard deviation. --- #### Data Set (a): **Data**: 2, 82, 47, 44, 72, 47, 70, 5, 37 **Calculations**: - **Mean**: __________ - **Variance**: __________ - **Standard Deviation**: __________ --- #### Data Set (b): **Data**: 58, 51, 59, 48, 46, 45 **Calculations**: - **Mean**: __________ - **Variance**: __________ - **Standard Deviation**: __________ --- #### Data Set (c): **Data**: 3.4, 4.2, 4.5, 2.9, 4.7 **Calculations**: - **Mean**: __________ - **Variance**: __________ - **Standard Deviation**: __________ --- ### Explanation - **Mean**: The average of the data set. - **Variance**: The measure of how much the data points are spread out from the mean. - **Standard Deviation**: The square root of the variance, indicating how much the data points typically deviate from the mean. To find these values, use the following formulas: 1. **Mean** \(\mu\) = \(\frac{\sum_{i=1}^{n} x_i}{n}\) 2. **Variance** \(\sigma^2\) = \(\frac{\sum_{i=1}^{n} (x_i - \mu)^2}{n}\) 3. **Standard Deviation** \(\sigma\) = \(\sqrt{\sigma^2}\) Where \(x_i\) represents each data point and \(n\) represents the number of data points in the set.
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