Types of Graphical Displays

Types of Graphical Displays

AP Statistics – Chapter 3 Topics

Assignments:

a. - 1, 3, 6, 12, 14

b. –15, 19, 20, 21

c. - 22, 27, 28, 31, 33

d. - 35, 36, 40, 41, 45

Types of Graphical Displays

Categorical Data

Bar Graphs, Comparative Bar Graphs

Pie Charts, Segmented Bar Graphs

Bar Graphs of Data organized by Year (or date)

Numerical Data

Dot-Plots

Stem and Leaf Charts, Back to Back Stem and Leaf

Histogram (Frequency and Relative Frequency), Cumulative Relative Frequency, Density

Scatterplot

Time Series

Under what circumstances might you choose one sort of graphical display over another? What are the advantages and disadvantages of each type of graphical display?

Be able to read and interpret a cumulative relative frequency plot.

If you want to compare two groups, what are the best graphical displays to use?

Calculate density.

Analyze and draw conclusions about the overall shape of a distribution. For example what might the distribution of the ages of the people at Lakehoma Elementary look like?

Skew Positively, Skew Negatively, Skew Right, Skew Left

Symmetrical

Unimodal, Bimodal, Multimodal

Outliers and Gaps

Where is the typical value(s) of a distribution? Bimodal distributions might have more than one “typical” value.

What does a uniform distribution look like?

What does a bell-shaped distribution look like?

What is the shape of a “normal” curve?

Draw general conclusions about the relationship between the x and y variables from a scatterplot.

Read and interpret a Time Series Plot.

Know the things that constitute an inappropriate visual display.

Penny Toss!

  1. Get into your groups.
  1. Each person should toss a penny toward the brick wall while standing the width of the sidewalk away. Try to get the penny as close to the wall as possible.
  1. Record how close to wall the penny ends up.
  1. Repeat this and have each person in the group toss the penny 10 times.

After you’ve tossed the pennies…

  1. Record all of the data for the entire class.
  2. Analyze the data by…
  • Creating a histogram (relative frequency or density)
  • Creating a cumulative relative frequency histogram and answering these questions.
  • Between what two distances are the middle 50% of coin tosses.
  • Half the coin tosses were closer than how far to the wall?
  • Where were the data the most spread out? In other words where was the most variability?
  1. What is the overall shape of the distribution of the distances?
  1. Are there any obvious outliers?
  1. If you eliminated the outliers would it change your analysis of the overall shape? If so, in what way would it change?
  1. Find the average distance for each player in your group.
  1. Repeat steps 3 through 5 for the set of all the class average distances.

Beyond Frequency Distributions and Histograms

The graph below displays the cumulative frequency of the lengths of phone calls made from the office at Mustang High.

  1. How many phone calls were made from the office this month?
  1. Estimate the median length of a phone call.
  1. What percentage of phone calls lasted more than 30 minutes?
  1. Make a frequency table for the length of phone calls data.
  1. Plot a histogram of this data.
  1. Describe the distribution of lengths of phone calls made from the math department offices.

The Attack of the Jellies!

Exploring similarities between sample histograms and population histograms.

Jellyblubbers have invaded my backyard! These small alien beings are threatening the very fabric of our society! They seem to be attacking in waves. Each attacking party is a subset of the population of Jellies. Since the social breakdown, based on Jelly length, of the colony of JellyBlubbers is part of the command and control structure, Jelly length is an essential element in the effectiveness of the fighting force. Therefore, an attacking party must look similar to the entire colony in terms of the distribution of JellyBlubber lengths in order to stand any chance of success.

In an effort to create such parties, the President of the Jellies has ordered that random sampling be used to select the members of each one. Following that the parties must be checked to insure a distribution of lengths similar to that of the colony. Only qualified parties will be allowed to attack.

Create a histogram of the lengths of all the JellyBlubbers in the colony. Then randomly select 7 parties of 25 JellyBlubbers each. Use histograms to check to see if the distribution of each sample is similar to that of the population.

A plot of the number of defective items produced during 20 consecutive days at a factory is shown below.


  1. Draw a histogram that shows the frequencies of the number of defective items.
  2. Give one fact that is obvious from the histogram but is not obvious from the scatterplot.
  3. Give one fact that is obvious from the scatterplot but is not obvious from the histogram.
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