AP Stat Do Now

1
AP Stat - Do Now

• In your notebook, write down all the different
  ways you learned about in Chapter 4 to display
  quantitative data.

2
Objectives

• Chapter 4 Displaying Quantitative Data
• What are some ways in which we can effectively
  display quantitative data?
• What can we learn about a distribution from its
  display?

NJCCCS 4.5.12.C.1
3
Objectives

• Chapter 4 Displaying Quantitative Data
• How do we describe a distribution?
• What are we looking for when comparing
  distributions?

NJCCCS 4.5.12.C.1
4
Dotplots

• A dotplot is a simple display. It just places a
  dot along an axis for each case in the data.
• Lets turn to the worksheet

5
Histograms

• First, slice up the entire span of values covered
  by the quantitative variable into equal-width
  piles called bins.
• The bins and the counts in each bin give the
  distribution of the quantitative variable.

6
Histograms

• A histogram plots the bin counts as the heights
  of bars (like a bar chart).
• Here is a histogram of the monthly price changes
  in Enron stock

Lets create a histogram using the worksheet
7
Histograms

• A relative frequency histogram displays the
  percentage of cases in each bin instead of the
  count.

8
Stem-and-Leaf Displays

• Stem-and-leaf displays show the distribution of a
  quantitative variable, like histograms do, while
  preserving the individual values.
• Stem-and-leaf displays contain all the
  information found in a histogram and, when
  carefully drawn, satisfy the area principle and
  show the distribution.

9
Stem-and-Leaf Displays
pulse rates of 24 women at a health clinic.
10
Constructing a Stem-and-Leaf Display

• First, cut each data value into leading digits
  (stems) and trailing digits (leaves).
• Use the stems to label the bins.
• Use only one digit for each leafeither round or
  truncate the data values to one decimal place
  after the stem.

11
Shape, Center, and Spread

• When describing a distribution, make sure to
  always tell about three things shape, center,
  and spread

12
What is the Shape of the Distribution?

• Does the histogram have a single, central hump or
  several separated bumps?
• Is the histogram symmetric?
• Do any unusual features stick out?

13
Humps and Bumps

• Does the histogram have a single, central hump or
  several separated bumps?
• Humps in a histogram are called modes.
• A histogram with one main peak is dubbed
  unimodal histograms with two peaks are bimodal
  histograms with three or more peaks are called
  multimodal.

14
Humps and Bumps (cont.)

• A bimodal histogram has two apparent peaks

15
Humps and Bumps (cont.)

• A histogram that doesnt appear to have any mode
  and in which all the bars are approximately the
  same height is called uniform

16
Symmetry

• Is the histogram symmetric?
• If you can fold the histogram along a vertical
  line through the middle and have the edges match
  pretty closely, the histogram is symmetric.

17
Symmetry (cont.)

• The (usually) thinner ends of a distribution are
  called the tails. If one tail stretches out
  farther than the other, the histogram is said to
  be skewed to the side of the longer tail.
• In the figure below, the histogram on the left is
  said to be skewed left, while the histogram on
  the right is said to be skewed right.

18
Anything Unusual?

• Do any unusual features stick out?
• Sometimes its the unusual features that tell us
  something interesting or exciting about the data.
• You should always mention any stragglers, or
  outliers, that stand off away from the body of
  the distribution.
• Are there any gaps in the distribution? If so, we
  might have data from more than one group.

19
Anything Unusual? (cont.)

• The following histogram has outliersthere are
  three cities in the leftmost bar

20
Where is the Center of the Distribution?

• If you had to pick a single number to describe
  all the data what would you pick?
• Its easy to find the center when a histogram is
  unimodal and symmetricits right in the middle.
• On the other hand, its not so easy to find the
  center of a skewed histogram or a histogram with
  more than one mode.
• For now, we will eyeball the center of the
  distribution. In the next chapter we will find
  the center numerically.

21
How Spread Out is the Distribution?

• Variation matters, and Statistics is about
  variation.
• Are the values of the distribution tightly
  clustered around the center or more spread out?
• In the next two chapters, we will talk about
  spread

Stay Tuned
22
Comparing Distributions

• Often we would like to compare two or more
  distributions instead of looking at one
  distribution by itself.
• When looking at two or more distributions, it is
  very important that the histograms have been put
  on the same scale. Otherwise, we cannot really
  compare the two distributions.
• When we compare distributions, we talk about the
  shape, center, and spread of each distribution.

23
Comparing Distributions (cont.)

• Compare the following distributions of ages for
  female and male heart attack patients

24
Timeplots Order, Please!

• For some data sets, we are interested in how the
  data behave over time. In these cases, we
  construct timeplots of the data.

25
Re-expressing Skewed Data to Improve Symmetry
Figure 4.11
26
Re-expressing Skewed Data to Improve Symmetry
(cont.)

• One way to make a skewed distribution more
  symmetric is to re-express or transform the data
  by applying a simple function
  (e.g., logarithmic function).
• Note the change in skewness from the raw data
  (Figure 4.11) to the transformed data (Figure
  4.12)

Figure 4.12
27
What Can Go Wrong?

• Dont make a histogram of a categorical
  variablebar charts or pie charts should be used
  for categorical data.
• Dont look for shape,
  center, and spread
  of
  a bar chart.

28
What Can Go Wrong? (cont.)

• Dont use bars in every displaysave them for
  histograms and bar charts.
• Below is a badly drawn timeplot and the proper
  histogram for the number of eagles sighted in a
  collection of weeks

29
What Can Go Wrong? (cont.)

• Choose a bin width appropriate to the data.
• Changing the bin width changes the appearance of
  the histogram

30
What Can Go Wrong? (cont.)

• Avoid inconsistent scales, either within the
  display or when comparing two displays.
• Label clearly so a reader knows what the plot
  displays.
• Good intentions, bad plot

31
What have we learned?

• Weve learned how to make a picture for
  quantitative data to help us see the story the
  data have to Tell.
• We can display the distribution of quantitative
  data with a histogram, stem-and-leaf display, or
  dotplot.
• Tell about a distribution by talking about shape,
  center, spread, and any unusual features.
• We can compare two quantitative distributions by
  looking at side-by-side displays (plotted on the
  same scale).
• Trends in a quantitative variable can be
  displayed in a timeplot.

32
AP Stat - Homework

• Read Chapter 4 if you have not already
• Quiz Chapter 3 on Friday
• Make sure that you have completed all your
  re-assessments by this Friday