When data is graphed it tends to naturally take what shape? List characteristics? (2)
- normal distribution -most points fall in centre, fewer towards extremes
What is an example of the naturally occurring standard distribution?
- Galton Board
What are the four characteristics of Normal Distribution?
1. symmetrical and bell-shaped 2. mean, median mode 3. asymptotic= extends forever without touching axis 4. area under the curve equals one
What are the two parameters of Normal Distribution?
1. mean 2. standard deviation
What are the normal distribution probabilities for 1, 2 and 3 standard deviations?
+/- 1= 68% +/- 2= 95% +/- 3= 99% anything after that is ~100%
What is a Z score?? (2)
1. A score that indicates how many standard deviations a raw score deviates from the mean 2. Comparisons relative to other participants
How do you interpret a Z score? (2)
1. Sign indicates above or below the mean ( left or right) 2. Magnitude indicates typical or atypical score!
What is an Atypical score and a typical score?
1. Atypical- outlier...not close to the mean... 2. Typical- closer to the mean...zero
What is the standard scores (z-scores) equation for populations and samples?
X=raw score to be standardized
X bar= mean of population
o= standard deviation of population
*** difference between z score pop and z score sample is that the z score sample has a S!...
Z scores are generally what?
- unit free.....allowing one to compare distributions that have different units...
Standard scores ( z scores) characteristics?
1. How many SD's a raw score varies from the mean
2. Directionality (+/-) = above or below mean
3. Magnitude = close or far from mean...
With every Z score question you should draw what??
-standard distribution curve ! to help with solving the question..
You can rearrange the z score formula to also solve for?
- the raw score.....
Z scores can determine the area associated with z scores and therefore the __________ are also possible to find.
The percentages of scores __ or ____ a given raw score.
- percentile rank
When looking at a Zscore chart......What does Comumn A, B and C represent?
- A: z score ( always positive )
-B: area between mean and z score
-C: area beyond the z score