Multiple Choice
Which characteristic must be known about a data set before the empirical rule can be applied?
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3. Describing Data Numerically
Standard Deviation
Multiple Choice
Which of the following sets of data will have the smallest ?
A
B
C
D
Verified step by step guidance1
Recall that the standard deviation measures the amount of variation or dispersion in a set of data values. A smaller standard deviation means the data points are closer to the mean.
Calculate the mean (average) of each data set using the formula: \(\text{mean} = \frac{\sum x_i}{n}\), where \(x_i\) are the data points and \(n\) is the number of points.
For each data set, find the squared differences from the mean: \((x_i - \text{mean})^2\) for each data point.
Calculate the variance by averaging these squared differences: \(\text{variance} = \frac{\sum (x_i - \text{mean})^2}{n}\).
The standard deviation is the square root of the variance: \(\text{standard deviation} = \sqrt{\text{variance}}\). Compare the standard deviations of each set to determine which is smallest.
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