Vocabulary: Individuals & Variables

Chapter 1 Outline Per:______________

The following is a small section of a data set describing education in the US.

CA PAC 35,894 499 519 54 18.9

CO MTN 4,601 551 553 27 11.3

CT NE 3,504 512 514 84 12.5

1. 
   Analyzing Categorical Data
   

What is the difference between a frequency table and a relative frequency table?

What is roundoff error?

The Bar Graph Things to remember: Make sure you label your axes and title your graph Scale your axes appropriately Each bar should correspond to the appropriate count. Leave room between bars.

The Pie Chart: Things to remember: Must include all the categories that make up the whole Counts will be percentages.

Example: Use the data to draw a bar graph AND a pie chart

340 320 409 389

When is it useful to use a bar graph?

Marginal Distribution:

Conditional Distribution:


Example: The table below gives information on the age and the number of school years completed for Americans (in thousands).

		Age Group
Education	25 to 34	35 to 54	55 and over	Total
Did not Complete HS	5325	9152	16035
Completed High School	14061	24070	18320
1 to 3 years of college	11659	19925	9662
4 or more years of college	10342	19878	8005
Total

1) What is the total number of people described by this table?

2) What percentage of Americans did not finish high school? (marginal)

3) What percentage of Americans between the ages of 35 to 54 completed high school? (marginal)

4) What percentage of Americans who had between 1 and 3 years of college are over 55? (conditional)

5) What percentage of Americans who are between 25 and 34 years old had only completed high school? (conditional)

5) Is there a relationship between age and whether or not one completed 4 years of college? (conditional)

6) Create a bar graph with the information in #5

2. 
   Displaying Quantitative Data with Graphs
   

Things to remember

• 
  You only need a properly labeled horizontal axis
  
• 
  Title the graph
  
• 
  Each dot represents a count of 1
  
• 
  Works well with a small data set
  

Runs Scored by the American league in the last 21 MLB All-Star Games

0	3	6	9	7	2	13	4	9	4	7
3	5	2	7	4	7	13	5	2	4

1. 
   The CENTER of the data
   

2. The SHAPE of the data

• 
  Symmetric
  

• 
  Skewed to the right
  
• 
  Skewed to the left
  

3. 
   The SPREAD of the Data
   

• 
  Range
  
• 
  IQR
  

Describe the overall pattern of the distribution of runs scored by the American League in the example above.

Things to remember

• 
  Separate each piece of data into a stem (all but the rightmost digit) and a leaf (the final digit).
  
• 
  Write the stems vertically in increasing order from top to bottom.
  
• 
  Write the leaves in increasing order out from the stem
  
• 
  Be very neat and make sure you leave the same amount of space in between leaves.
  
• 
  Title your graph
  
• 
  Include a key identifying what the stem and leaves represent.
  

• 
  Works well with a small data set
  

Example:

When is it advantageous to split stems in a stemplot?

Things to remember:

• 
  It is the most common graph of a quantitative variable.
  
• 
  The x-axis is continuous, so there should be no gaps between the bars (unless a class has zero observations)
  
• 
  Title your graph
  

How to make a histogram:

• 
  Divide the range of data into classes of equal width
  
• 
  Find the count (frequency) or percent (relative frequency) of individuals in each class
  
• 
  Label and scale your axes and draw histogram
  

Example: NBA Scoring Averages

How is the stemplot of a distribution related to its histogram?

What is the difference between a bar graph and a histogram?

When is it better to use a histogram rather than a stemplot or dotplot?

• 
  The most common measure of center
  
• 
  The mean is the arithmetic average.
  
• 
  To find the mean of a set of observations you use the following formula:
  

Important things to remember:

• 
  Although most common, not always most appropriate measure
  
• 
  Very sensitive to outliers
  
• 
  If a distribution is skewed, the mean will not be an accurate measure of center
  

• 
  The _______________ of a distribution
  
• 
  The measure of center which is resistant to _________________ and _____________________
  
• 
  To find the median of a distribution:
  
  1. 
     Arrange observations in order from ______________ to ___________________
     
  2. 
     If the number of observations is odd, the median is the center observation in the ordered list
     
  3. 
     If the number of observations is even, the median is the average of the two center values in the ordered list
     

• 
  The mean and median in a symmetric distribution will be very close to each other.
  
• 
  If a distribution is exactly symmetric, the median and mean __________________________________
  
• 
  If a distribution is skewed to the left, the mean will _________________________________________
  
• 
  If the if the distribution is skewed to the right, the mean will __________________________________
  

• 
  The difference between the largest and smallest observation (max – min).
  
• 
  Useful if there are no outliers.
  

• 
  The range of the middle __________________
  
• 
  To calculate the quartiles:
  

1. 
   is the median of the bottom half of the observations. It separates the bottom ___% of observations from the top ____%.
   
2. 
   is the median of the top half of the observations. It separates the top ___% of observations from the bottom ___%.
   
3. 
   IQR: _____________
   

An observation is an outlier if it falls:

• 
  Less than __________________________________
  

• 
  Higher than _____________________________________
  

• 
  _________________
  
• 
  _________________
  
• 
  _________________
  
• 
  _________________
  
• 
  _________________
  

Here is data for the amount of fat (in grams) for each of McDonald’s different chicken sandwiches:

• 
  From the graph, we can see center, shape, and spread
  
• 
  How to Construct a BoxPlot:
  

• 
  A central box is drawn from the first quartile to the third quartile
  
• 
  A line in the box marks the median
  
• 
  Lines (whiskers) extend from the box out to the smallest and largest observations that aren’t outliers.
  

1. 
   Find the distance of each observation from the mean and square each of these distances
   
2. 
   Average the distances by dividing their sum by n-1
   
3. 
   is the square root of this average squared distance
   

• 
  The median and IQR are used when describing __________________________________
  
• 
  The mean and standard deviation are used when describing ___________________________