To calculate the population standard deviation (stdevp) of the value 2067.79 and the mean of 241 (which is the result of \( 5784 \div 24 \)), we need to follow these steps:
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Calculate the population mean: This was already given as 241.
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Calculate the variance: The variance is given by the formula: \[ \sigma^2 = \frac{1}{N} \sum (x_i - \mu)^2 \] where \( N \) is the number of data points, \( x_i \) are the individual data points, and \( \mu \) is the mean.
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Data Points: In this case, you have two data points: 2067.79 and 241.
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Calculate the differences from the mean and square them:
- For 2067.79: \[ (2067.79 - 241)^2 = (1826.79)^2 = 3331934.0641 \]
- For 241: \[ (241 - 241)^2 = 0^2 = 0 \]
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Sum the squared differences: \[ 3331934.0641 + 0 = 3331934.0641 \]
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Calculate the variance: Since there are 2 data points: \[ \sigma^2 = \frac{3331934.0641}{2} = 1665967.03205 \]
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Calculate the population standard deviation: \[ \sigma = \sqrt{1665967.03205} \approx 1291.89 \]
Thus, the population standard deviation (stdevp) of the values 2067.79 and 241 is approximately 1291.89.
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