Chapter 2

Measures of center: median, mean

1. State the formula for the sample mean of a data set.
2. Recognize the notation \(\bar{x}\) for the sample mean.
3. Compute the sample mean of a (small) data set by-hand.
4. State a physical interpretation of the sample mean in terms of the rug plot of the data.
5. State the definition of the sample median.
6. Compute the sample median of a (small) data set by-hand.

Measures of spread: percentiles, standard deviation

1. State the formula for the sample variance and sample standard deviation.
2. Recognize the notation \(s\) for the sample standard deviation.
3. Compute the sample variance and sample standard deviation of a (small) data set by-hand.
4. Define the sample quartiles of a data set.
5. Recognize the notation \(Q_{1}\), \(Q_{2}\), and \(Q_{3}\) for the first, second, and third sample quartiles.
6. Define the interquartile range of a data set.

Graphical displays of numerical summaries

1. State the five components of the “five-number summary.”
2. Draw a boxplot for a data set given a five-number summary of the data set.
3. Interpret a boxplot in terms of symmetry versus skewness of a distribution and identification of outliers.

R

1. Compute the sample mean, sample median, sample standard deviation, and five-number summary using mosaic in R.
2. Plot a boxplot using mosaic in R.