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Understanding Statistical Summaries and Histograms: Key Concepts

Explore the relationship between mean, median, standard deviation, and quartiles in histograms. Learn how outliers impact mean and median placement and the effects of data transformation on statistical measures.

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Understanding Statistical Summaries and Histograms: Key Concepts

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  1. Stat 135 Lab 7 Learning objective #38 TA: Dongmei Li

  2. Lecture Review • Symmetric • Mean=Median • Skewed to the left • Mean < Median • Skewed to the right • Median < Mean • The mean and standard deviation are heavily influenced by outliers, the median and the quartiles are not. Because of this, the mean is located farther toward the long tail of a skewed histogram than the median.

  3. Lecture Review • Boxplot • Min • Max • Q1 • Q3 • Median

  4. Lecture Review • When the standard deviation = 0, there is no spread – every number on the list is the same. • Adding or subtracting the same value to every number on a list will change the median and mean correspondingly, but not the standard deviation. • Multiplying or dividing every number on a list by the same positive value will change the mean, median, and standard deviation correspondingly. • Multiplying or dividing by a negative value will change the standard deviation by the corresponding positive number (the standard deviation is always positive).

  5. Lab 7 Learning Objective • 38. Learn the relationship between key statistical summaries and histograms (For example, mean, median, standard deviation, and quartiles).

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