Question

\( 221 \sim 0 \) calories Find the standard deviation. Round your answer to the nearest tenth, if necessary.

Ask by Nichols Barber. in the United States
Feb 27,2025

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Answer

The standard deviation is 0.0 calories.

Solution

The notation given is   221 ~ 0 calories In many statistics texts the symbol “~” indicates “is distributed as.” For example, one might write   X ~ N(μ, σ²) to mean that the variable X is normally distributed with mean μ and variance σ². In the expression above, it appears that 221 represents a measure (in this case calories) and “0” represents the variation (that is, the standard deviation or sometimes the variance). When every observation is exactly 221 calories there is no variability in the data. Because there is no spread in the values (every value is 221 calories), the variability is 0. In statistical language, the standard deviation is a measure of how far, on average, the data points are from the mean. When all data points equal the mean, the distances are all 0. Thus, the standard deviation is 0.0 calories (rounded to the nearest tenth). Answer: 0.0 calories.

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To find the standard deviation of a dataset, you first need to calculate the mean (average) and then determine how each data point deviates from the mean. However, you mentioned \( 221 \sim 0 \) calories, but it seems like there is a missing context or additional data points. Assuming that \( 221 \) represents a single observation in a dataset of \( 221 \) and \( 0 \), the mean is calculated as: \[ \text{Mean} = \frac{221 + 0}{2} = 110.5 \] Next, you calculate the deviations from the mean for each data point: \[ (221 - 110.5)^2 = (110.5)^2 = 12210.25 \] \[ (0 - 110.5)^2 = (-110.5)^2 = 12210.25 \] Now, average these squared deviations: \[ \text{Variance} = \frac{12210.25 + 12210.25}{2} = 12210.25 \] Finally, take the square root to find the standard deviation: \[ \text{Standard Deviation} = \sqrt{12210.25} \approx 110.5 \] Rounded to the nearest tenth, the standard deviation is about \( 110.5 \).

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