Lesson 4: Bell-Shaped Curves and Statistical Pictures

Lesson Overview Section

In Lesson 4 we continue our discussion of describing data through numerical summaries and also think about statistical pictures.  An overview of some key questions addressed is given in the table below.

Question Addressed Statistical Summary
Where are values located along the number line?

Median

Mean

How variable are the numbers?

IQR

Standard Deviation

What is the relative standing of an individual value compared with other numbers on a list?

Percentiles

Standardized Scores

Question Addressed Statistical Picture
How are all of the numbers on a list distributed over the number line?

Dot plots

Boxplots

Histograms
(normal or bell-shaped curve is a special case)

How is a categorical variable distributed?

How do categorical variables compare?

Bar graphs

Comparative bar graphs

How do the distributions of two measurement variables compare?

Comparative boxplots

Comparative dotplots

How do percentages or averages change over time? Line graph or time series plot
How are two measurement variables associated? Scatterplot

Objectives

After successfully completing this lesson, you should be able to:

  • Interpret standard scores as a measure of relative standing on a list.
  • Apply the relationship between standard scores and the percentiles of a normal distribution.
  • Interpret graphs used with categorical data.
  • Interpret scatter plots.
  • interpret time series plots and recognize trends and seasonality.
  • critique whether graphical presentations provide a fair summary of the data.