Lesson 1 Summary

• The choice of the right sample and sample size is the most important factor in statistical analysis. A manager should always ask about the sample size and sample characteristics. The sample must be a true representation of the population under question. Intentionally or unintentionally selecting only a subset of the population leads to less reliable results, and is often the reason people are skeptical about “statistical predictions.”
• Mean, median, and the mode are measures of centrality of the data. Few extreme data points (outliers) skew the data. The mean is sensitive to outliers, while the median is not.
• The 5-number summary of a data consists of the minimum, maximum, and median and the 25th and 75th percentiles.
  • The 5-number summary can be graphically displayed with a box (also known as box-and-whisker) plots.
• Standard deviation measures how spread out the numbers are from the mean.
  • Standard deviation may serve as a measure of uncertainty or risk.
  • Quality control efforts are often aimed at reducing the standard deviation (i.e., increasing the predictability of a process).
• Which measure of variation to use?
  • There are three main measures of variability—variance, standard deviation, and range.
    • standard deviation is more often used over variance because it is directly interpretable. It has the same units as the data.
    • range tells us the difference between the minimum and maximum data points, but does not tell much about how dispersed the data is.
    • coefficient of variation is very useful (standard deviation/mean) when it comes to comparing disparate sets of data.
• Histograms and frequency distributions are common ways of visualizing the data.
  • A histogram is a bar chart where the data is grouped in ranges.
  • A frequency distribution shows the number of times a particular value occurs in the data.
  • Relative frequency distributions show the percentage of times a particular value occurs in the data.