Lecture 5: The Normal Distribution, Z-scores, And Percentiles Flashcards
What’s a normal distribution? (Describe shape and characteristics!)
A type of bell shaped, symmetric, unimodal distribution
Give examples of common variables in nature that have an approximately normal distribution
- Height
- Resting HR
- Weight
- Body temperature
Give examples of test instruments that are deliberately calibrated so scores have an approximately normal distribution
- IQ Scores
- SAT scores
In the normal distribution the mean, median, and mode are _____?
THE SAME!!
Whats the z-score?
The number of standard deviations from the mean away
How to convert to a z-score?
Subtract the mean from the value than divide the result by the standard deviation!
How to convert from a z-score to a value on the original scale of the variable?
Multiply the z-score by the standard deviation and add the mean to the result!
Where is 1 standard deviations from the mean located on a normal curve?
AT THE INFLECTION POINT! - Where the curve switches between more cupped-up and more cupped-down
Whats the approximate percentages of values in between -1 to 1 standard deviations from the mean
68%
Whats the approximate percentages of values in between -2 to -1 or from 1 to 2 standard deviations from the mean?
13.5%
Whats the approximate percentage of values that is lower than -2 or higher than 2 standard deviations of the mean?
2.5%
How much percentage of values are above -2 and below 2 standard deviations of the mean?
95%!
What are percentiles?
Percentiles express what percentage of scores are below a given score eg.
- 90th percentile is the score higher than 90% of scores
What’s the 50th percentile?
The score that is higher than 50% of scores but ALSO the MEDIAN!
