A psychology survey reports that the standard deviation of reaction times for the entire sample is 2.82.8 seconds, while the standard deviation for male respondents is 2.32.3 seconds and for female respondents is 2.12.1 seconds. Which reason most directly explains why the combined standard deviation exceeds the subgroup standard deviations?

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1. Intro to Stats and Collecting Data(0)

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Levels of Measurement
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Intro to Collecting Data
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Sampling Methods
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2. Describing Data with Tables and Graphs(0)

Visualizing Qualitative vs. Quantitative Data
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Frequency Distributions
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Histograms
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Bar Graphs and Pareto Charts
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Time-Series Graph
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3. Describing Data Numerically(0)

Mean
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Median
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Mode
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Standard Deviation
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Interpreting Standard Deviation
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Percentiles & Quartiles
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Introduction to Confidence Intervals
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Determining the Minimum Sample Size Required
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3. Describing Data Numerically

Standard Deviation

3. Describing Data Numerically

Standard Deviation: Videos & Practice Problems

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Problem 94Multiple Choice

A psychology survey reports that the standard deviation of reaction times for the entire sample is $2.8$ seconds, while the standard deviation for male respondents is $2.3$ seconds and for female respondents is $2.1$ seconds. Which reason most directly explains why the combined standard deviation exceeds the subgroup standard deviations?

The combined standard deviation exceeds subgroup values because taking groups separately reduces measurement error to zero.

The combined standard deviation exceeds subgroup values because variances should always be added rather than averaged.

The combined standard deviation exceeds subgroup values because the between-group differences in means increase total variance

The combined standard deviation exceeds subgroup values because one subgroup must have a much larger sample size.

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