객관식
Given a population with mean = and standard deviation = , what is the z-score of a value = ?
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3. Describing Data Numerically
Standard Deviation
Multiple Choice
Given the following two samples: Sample 1: and Sample 2: , what is the value of the pooled standard deviation for these data sets?
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검증된 단계별 안내1
Calculate the sample size for each group. For Sample 1, count the number of data points (n_1), and for Sample 2, count the number of data points (n_2).
Compute the sample variance for each sample. First, find the mean of each sample using the formula \(\bar{x} = \frac{\sum x_i}{n}\). Then calculate the variance \(s^2\) for each sample using \(s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}\).
Use the formula for the pooled variance, which combines the variances of the two samples weighted by their degrees of freedom:
\( s_p^2 = \frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2} \)
Take the square root of the pooled variance to find the pooled standard deviation:
\( s_p = \sqrt{s_p^2} \)
Interpret the result as the combined estimate of the standard deviation for the two samples, which accounts for the variability within each sample and their sizes.
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