displaying quantitative data ap stats nhs mr. unruh
Post on 21-Jan-2016
219 Views
Preview:
TRANSCRIPT
Displaying Quantitative Data
AP STATS
NHS
Mr. Unruh
Slide 4- 5
Dotplots• A dotplot is a simple display. It just places a dot along an axis for each case in the data.
• The dotplot to the right shows Kentucky Derby winning times, plotting each race as its own dot.
• You might see a dotplot displayed horizontally or vertically.
Slide 4- 9
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 leaf—either round or truncate the data values to one decimal place after the stem.
Slide 4- 10
Stem-and-Leaf Example
• Compare the histogram and stem-and-leaf display for the pulse rates of 24 women at a health clinic. Which graphical display do you prefer?
Dealing With a Lot of Numbers…
• Summarizing the data will help us when we look at large sets of quantitative data.
• Without summaries of the data, it’s hard to grasp what the data tell us.
• The best thing to do is to make a picture…
• Bar charts and Pie Charts are for qualitative data
Slide 4- 13
Histograms: Displaying the Distributionof Price Changes (cont.)
• 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:
Slide 4- 14
Slide 4- 15
Histograms: Displaying the Distributionof Price Changes (cont.)
• A relative frequency histogram displays the percentage of cases in each bin instead of the count.
• In this way, relative
frequency histograms are faithful to the area principle.
• Here is a relative frequency histogram of the monthly price changes in Enron stock:
Slide 4- 16
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.
Examining a Distribution
• Look for the following:
• Shape - Does the distribution have one or more peaks (modes) or is it unimodal?
• Outliers – an individual value that falls outside the overall pattern.
• Center – What number is the data centered around?
• Spread - Is the distribution approximately symmetric or is it skewed in one direction? Is it skewed to the right (right tail longer) or left?
Slide 4- 18
Think Before You Draw, Again
• Remember the “Make a picture” rule?
• Now that we have options for data displays, you need to Think carefully about which type of display to make.
• Before making a stem-and-leaf display, a histogram, or a dotplot, check the• Quantitative Data Condition: The data are values of a quantitative
variable whose units are known.
Slide 4- 19
Describing a distribution of dataWhen describing a distribution, make sure to always tell about four things:
1.) Shape
2.) Outliers
3.) Center
4.) Spread
Slide 4- 20
Humps and Bumps
1. 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.
Slide 4- 21
What is the Shape of the Distribution?
1. Does the histogram have a single, central hump or several separated bumps?
2. Is the histogram symmetric?
3. Do any unusual features stick out?
Slide 4- 22
Humps and Bumps (cont.)
• A bimodal histogram has two apparent peaks:
Slide 4- 23
Humps and Bumps (cont.)
• A histogram that doesn’t appear to have any mode and in which all the bars are approximately the same height is called uniform:
Slide 4- 24
Symmetry
2. 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.
Slide 4- 25
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.
Slide 4- 26
Where is the Center of the Distribution?
• If you had to pick a single number to describe all the data what would you pick?
• It’s easy to find the center when a histogram is unimodal and symmetric—it’s right in the middle.
• On the other hand, it’s 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.
Slide 4- 27
Anything Unusual?
3. Do any unusual features stick out?• Sometimes it’s 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.
Slide 4- 28
Anything Unusual? (cont.)
• The following histogram has outliers—there are three cities in the leftmost bar:
Slide 4- 29
Comparing Distributions (cont.)• Compare the following distributions of ages for female and male heart attack patients:
Slide 4- 30
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.
Slide 4- 31
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.
Slide 4- 32
*Re-expressing Skewed Data to Improve Symmetry
Figure 4.11
Histogram of the average age of U.S. Presidents at Inaugaration
• The purpose of an Exploratory Data Analysis is to organize data and identify patterns/departures.
• PLOT YOUR DATA - Choose an appropriate graph
• Look for overall pattern and departures from pattern
• Shape {mound, bimodal, skewed, uniform}
• Outliers {points clearly away from body of data}
• Center {What number “typifies” the data?}
• Spread {How “variable” are the data values?}
top related