Comparing data sets

Misleading statistics and biased samples, summary statistics, shape and skewness, and comparing two data sets with parallel box plots.

Misusing statistics

Watch for small or biased samples, graphs whose vertical axis does not start at zero, and averages that hide outliers. Always ask who collected the data and why.

Shape

Comparing with box plots

Example 1●●

Class A test scores have median $68$ and IQR $12$. Class B has median $74$ and IQR $25$. Compare them.

Class B scored higher on average (larger median).

Class A's results were more consistent (smaller IQR).

Flashcards

Positive skew

Tail to the right

Compare two groups using

Centre and spread

Misleading graph trick

Axis not starting at zero

Practice

Class A: median $68$, IQR $12$. Class B: median $74$, IQR $25$. Which class was more consistent?
Which class scored higher on average?
Incomes usually have a long tail of very high earners. The data is:
IQR of $4, 6, 7, 9, 10, 12, 15$?
Scores on an easy test, mostly high with a few low ones, are:
In positively skewed data the mean is usually:
A poll of $20$ people outside a gym claims "$90\%$ of Australians exercise daily". The main problem is:
Median of $4, 6, 7, 9, 10, 12, 15$?