Chapter 5: Describing Distributions Numerically

Question 1

What are some ways to compare distributions?

Answer 1

• Compare distributions of 2 or 3 groups with histograms.
• Compare several groups with boxplots, which make it easy to compare centres and spreads and spot outliers, but hide much of the detail of distribution shape.

Question 2

How should we treat outliers?

Answer 2

With attention and care.

• When we group data in different ways, different cases may emerge as outliers.
• Track down the background for outliers - it may be informative.

Question 3

What can re-expression of data do and what are some ways to do it?

Answer 3

• Re-expression can make skewed distributions more nearly symmetric.
• Re-expression can make the spreads of different groups more nearly comparable.
• For right-skewed data, try sqrt, logs, or reciprocals. For left-skewed data, try squaring or exponential function.

Question 4

When comparing the distributions of several groups using histograms or stem-and-leaf displays, consider their…?

Answer 4

• Shape
• Centre
• Spread

Question 5

When comparing groups with boxplots, compare the…?

Answer 5

-Compare the shapes. Do the boxes look symmetric or skewed? Are there differences between groups?
-Compare the medians. Which group has the higher centre? Is there any pattern to the medians?
-Compare the IQRs. Which group is more spread out? Is there any pattern to how the IQRs change?
Using the IQRs as a background measure of variation, do the medians seem to be different, or do they just vary in the way that you’d expect from the overall variation?
-Check for possible outliers. Identify them if you can and discuss why they might be unusual. Of course, correct them if you find that they are errors.

Question 6

Define ‘Timeplot’.

Answer 6

A timeplot (often called a time series plot) displays data that change over time. Often, successive values are connected with lines to show trends more clearly. Sometimes a smooth curve is added to the plot to help show long-term patterns and trends.