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Section: M1.1.3

Measures of center

• Recall how to calculate mean and median.
• Understand mean and median as a “typical value” that can answer a statistical question.
• Know that mean and median are equal for a symmetrical data distribution.
• Explain why mean and median are unequal for a skewed data distribution.
• Select mean as the better measure for symmetrical distributions, and median as the better measure for skewed distributions.
• Make generalization what kinds of distributions have means larger than medians, and what kinds have medians larger than means.
• Recognize outliers when they exist, and know to investigate their source—that data point is way out there, why is that? Is there something weird about it that means we should disregard it?
• Know that outliers affect the mean, but not the median of a data set.

Instead of creating representations of data, the emphasis in high school is on interpreting representations and judiciously interpreting measures of center and spread. Students describe the shape of a data distribution in more detail (symmetric, skewed, flat, or bell-shaped). Students develop a more precise understanding of measures of center and understand relationships between mean and median for symmetrical and skewed data distributions. They learn that outliers affect the mean of a data set but not the median. They recognize outliers when they exist and learn to investigate their source. Students learn that standard deviation is a measure of spread, that a larger standard deviation means the data are more spread out, and to understand standard deviation as “typical distance from the mean” for a symmetrical distribution. They also understand that interquartile range is a description of variability better-suited to a skewed distribution. Finally, students are introduced to two-way frequency tables and understand how to interpret relative frequencies in the context of the data represented in the tables.

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