What is "statistics"?

The science of conducting studies to 
collect, organize, summarize and analyze data
in order to draw conclusions.

Collecting Data

    Data can be observational or experimental.  There are a variety of ways to collect data.  For this lesson, we will collect data using a survey tool.  Though one of the items will require taking a measurement.  Click here for the survey.

Organizing Data

    There are a variety of ways to help you organize your data.  You can list variables in increasing order, count frequencies using a tallies and use charts to help divide counts into similar groups.  We will examine various ways to help organize the data as well as represent the data.

Stem-and-Leaf Plots   

Description

 

 

Example:  Heights

 

 

 

 

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Representing Data

    We will study ways to represent the data numerically as well as graphically.  We will use the data collected from the survey for our examples.   We will take notes and work examples on some of the items listed below.

Descriptive Statistics    (Numerical Representation of the Data)

• Measures of Central Tendency
  • Mean
  • Median
  • Mode
• Measures of Variation
  • Range
  • Interquartile Range
  • Standard Deviation
• Measures of Location
  • Percentiles
  • Z-Scores

Graphical Representations 

• Numerical Data
  • Dot Plots - show distribution of data
  • Stem-and-Leaf Plots - show distribution
  • Histograms - show frequency or percent of time a range occurs; also show distribution
  • Scatterplots - show relationship between two numerical variables
  • Box Plots - show spread of data & extreme observations

• Categorical Data
  • Bar Charts - show frequency or percent of time a category occurs; also show distribution
  • Pie Charts - show frequency or percent of time a category occurs
  • Line Graphs - show trends, sometimes over time
  • Cross Tabulations - help count number of items in multiple categories

Describing the Distribution of the Data    

• General Shapes of Distributions
  • Mound Shaped
  • Symmetrical
  • U-shaped
  • Bi-modal 
  • Skewed
    • Skewed Right
    • Skewed Left
• Special Case
  • Normal Distribution
    • The Empirical Rule (Relating Means and Standard Deviations)
    • Example:  If a test is normally distributed with a mean of 75 and a standard deviation of 5 points, what percent of the students make a C?  What percent of students make an A or a B?   

     

Statistics Related Problems in You Textbook

        4th Grade:  Bar Charts, Pie Charts, Tallies, Line Charts, Pictographs, Averages
        5th Grade:  Bar & Line Graphs (Using Information to Solve Problems.)  Averages.

Formulate and Test Hypothesis to Draw Conclusions  (Statistics Strand Grades 6-8)

It is important to have a general idea about statistical hypotheses testing.  For example, statistical hypothesis testing is used to determine whether a new medicine will have the desired result on a set of patients.  Now that pharmaceutical commercials are on television, it is useful to know a little about the statistical tests that are used to determine if, for example, the occurrence of a certain side effect does not occur "significantly more often then with sugar pills." 

Difference in Heights Example 

1) Form a Hypothesis (after doing a literature review or pilot study)

            Example Research Hypotheses:  The average height of students in the fifth grade is significantly more than the average height of students in the fourth grade.

            Null Hypothesis: _________
            Alternative Hypothesis:  ________

2) Collect Data that you believe will help you prove whether the hypothesis is true of false.

            We will modify our hypothesis to determine the difference in the heights of fourth and fifth grade teachers.  We have already recorded your heights.

3)  Organize the data and find the descriptive statistics.  

4)  Use the descriptive statistics to compare the two groups and see if the differences in the sample averages are "significantly different."  You will also need to use the standard deviation to determine how spread out the data are.  This is where the statistics formulas and tables are used.

    Example

5)  State your conclusion to the problem in the context of the problem.  This is a great place to integrate writing in the math classroom. 

[Next: Probability]