Unit 2 Glossary
Vocabulary Words
Intra-Quartile Range (IQR): The distance between the 3rd quartile and the first quartile.
first quartile: The value that has 75% of all observed values above it and 25% below it.
five-number summary: A list of the five quartiles.
influential outlier: An outlier that drastically changes the results.
intra-quartile range (IQR): The third quartile minus the first quartile; i.e., the size of the range where the middle half of the data is.
lower fence: 1.5 IQRs below the 1st quartile
more extreme: Further away from the mean.
outliers: Values on the observed data that are far more extreme than others, either due to luck or to a problem in the data measurement.
quartiles: The five cutoff values that split the observed data into 4 sections with equal observations: Min, Q1, Median, Q3, Max.
sample standard deviation: The estimated standard deviation, calculated by looking at how far observed values fall from the sample mean.
sampling variability: The idea that results from one random sample will be different than results from another, even if the population is the same.
standard deviation: The typical distance that an observed value is expected to be away from the mean.
standard deviation of the sample proportion: The typical distance that a sample proportion falls from the true (population) proportion.
third quartile: The value that has 25% of all observed values above it and 75% below it.
upper fence: 1.5 IQRs above the 3rd quartile.
variance: The standard deviation squared; calculated by finding the average squared distance between observed values and the mean.
z-score: The number of standard deviations a value is from the mean.
Key Skills and Concepts
- Use a summary or plot of a population to determine likely and unlikely results in a sample.
- Calculate or approximate how many standard deviations a particular value is from the mean.
- How far we expect a sample mean to be from the true (population) mean.
- Calculate the standard deviation of a sample mean of a variable, if you know the standard deviation of the variable itself.
- Values within 2 or so standard deviations of the true mean are not very uncommon; values with z-scores of 3 or above are quite unlikely.
- Know the symbols for one observed value, the standard deviation of an observed value, the sample mean, the true mean, and the standard deviation of the sample mean.
- Make arguments about a claim by saying how unlikely our observed data would be if the claim were true.
- Make an argument for which of two claims is true, based on which one is more likely to produce the data you observe.
- Estimate the standard deviation by looking at typical distances between observed values and the sample mean.
- A less common measure of variability, equal to the average absolute value of the distance between observed values and the mean.
- Describe the shape of the observed values - such as skew - from a five-number summary.
- Carefully consider if an outlier is valuable data, even though it is extreme, or if it should be removed.