Transcript Caitlin`s Seminar

Seminar Eight
Individual Z-Scores and
Z-Score Patterns
Caitlin Crawford
September 20, 2007
Calculating Z-Scores
• All female heights have mean 65 and standard
deviation 2.5
• All male heights have mean 70 and standard
deviation 3
• Formula: z=(x-µ)/σ
• In other words, the mean subtracted from
your value, divided by the standard deviation
Constructing a Histogram
• A histogram display values of a quantitative
variable with vertical bars showing the count
of values in certain interval ranges.
• Steps:
1. Divide range of data into intervals of equal width
2. Find the count of observations in each interval.
3. Draw the histogram, using the horizontal axis for range of
data and vertical axis for count
Commenting on Histogram
• Are there large negative or positive z-scores?
• What percentage of z-scores are less than 1, 2,
or 3?
- 68% of z-scores are between 1 and -1
- 95% of z-scores are between 2 and -2
- 99.7% of z-scores are between 3 and -3
• Do our results conform to 68-95-99.7 rule?
• Would results differ for a larger class?
Example Two
• How many minutes (to the nearest 10
minutes) did you spend doing homework
yesterday?
Calculating Mean and
Standard Deviation
Steps for calculating by hand:
1. Find the mean (add up all the numbers and
divide by how many there are)
2. Find the deviations from the mean
3. Find the squared deviations from the mean
4. “Average” the squared deviations, dividing
their sum by the number of observations-1
5. Take the square root of the variance to find
the standard deviation
Calculating Z-Scores
• Use a calculator to find your individual z-score
• Formula: z=(x-µ)/σ
• In other words, the mean subtracted from
your value, divided by the standard deviation
Constructing a Histogram
• A histogram display values of a quantitative
variable with vertical bars showing the count
of values in certain interval ranges.
• Steps:
1. Divide range of data into intervals of equal width
2. Find the count of observations in each interval.
3. Draw the histogram, using the horizontal axis for range of
data and vertical axis for count
Commenting on Histogram
• Are there large negative or positive z-scores?
• What percentage of z-scores are less than 1, 2,
or 3?
- 68% of z-scores are between 1 and -1
- 95% of z-scores are between 2 and -2
- 99.7% of z-scores are between 3 and -3
• Do our results conform to 68-95-99.7 rule?
• Would results differ for a larger class?
Example Three
• How many hours of sleep did you get last
night?
-Please round to the nearest half hour
Calculating Mean and
Standard Deviation
Steps for calculating by hand:
1. Find the mean (add up all the numbers and
divide by how many there are)
2. Find the deviations from the mean
3. Find the squared deviations from the mean
4. “Average” the squared deviations, dividing
their sum by the number of observations-1
5. Take the square root of the variance to find
the standard deviation
Calculating Z-Scores
• Use a calculator to find your individual z-score
• Formula: z=(x-µ)/σ
• In other words, the mean subtracted from
your value, divided by the standard deviation
Constructing a Histogram
• A histogram display values of a quantitative
variable with vertical bars showing the count
of values in certain interval ranges.
• Steps:
1. Divide range of data into intervals of equal width
2. Find the count of observations in each interval.
3. Draw the histogram, using the horizontal axis for range of
data and vertical axis for count
Commenting on Histogram
• Are there large negative or positive z-scores?
• What percentage of z-scores are less than 1, 2,
or 3?
- 68% of z-scores are between 1 and -1
- 95% of z-scores are between 2 and -2
- 99.7% of z-scores are between 3 and -3
• Do our results conform to 68-95-99.7 rule?
• Would results differ for a larger class?
The End
Thanks for your
participation!