Below is an outline of the lesson with italicized comments enclosed in square brackets [like this].
—Normal
Model
·
Which is more unusual?
o
Discuss as class, how could these be compared? [Compare someone walking into the room who is 82" tall or with a show size of 4.]
·
Quick investigation [Went as described, allows to see students where z-score is derived.]
o
Pick 5 different values
o
Calculate the mean and standard deviation
o
Now, add a value of 9 to each original value
§
What happens to mean and standard deviation
o
Next, subtract a value of 9 from each original
value
§
What happens to mean and standard deviation
o
Multiply each original value by 9
§
What happens to mean and standard deviation
o
Divide each original value by 9
§
What happens to mean and standard deviation
·
What will the mean and standard deviation be if
you subtract x-bar from each datum
o
Mean is zero, standard deviation unchanged
·
What will the mean be if you divide transformed
data by the standard deviation
o
Mean is zero and standard deviation one
o
What are the units of this transformed data [Students need to realize that z-scores are unitless.]
o
This is known as a z-score
·
What is the meaning of the z-score
o
Tells how many standard deviations a value is
away from the mean
·
Going back to opening question, what if we
calculate the z-score for both items? [Didn't have data, used their 5 numbers that they picked.]
o
Can compare to see which is more unusual
·
Work with z-scores on worksheet
·
The distribution of z-scores is known as the
standard normal model [Used 15 z-scores from their randomly selected numbers and created a histogram. Students described distribution as unimodal with a slight left skew.]
o
Mean is zero and standard deviation is one
·
Calculate areas under curve [Worked through several examples using a z-table.]
o
Using table
o
Using 68.26, 95.44, 99.74 rule
·
Practice with normal model worksheet
No comments:
Post a Comment