Ch 2 Flashcards
Percentile
the pth percentile of a distribution is the value w/ p percent of the observations less than it (# of people below you divided by the total)
% of ppl below you
graph to show percentiles
Relative Cumulative Frequency Graph or an Ogive
Standardized score (z-score)
if x is an observation from a distribution that has a known mean and standard deviation, the standardized score for x is
z= (x-mean)/sx
what does the z-score (standardized score) tell you?
how many standard deviations a value is from the mean
Effects of adding (or subtracting) a constant
+ same positive #a to each observation (or subtracting a from)
+ a to or - a from measure of center and location
does NOT change shape or measures of spread
effects of multiplying (or dividing) by a constant
x or dividing each observation by same positive # b
x or divides measures of center and location by b
x or divides measures of spread by b
does NOT change shape of distribution
different between x & divid. and + & - by a constant
+ and - doesnt change shape or spread
x & divid. doesnt change shape
Density Curve
model of the data (describes the overall pattern of a distribution)
what are density curves like a model of?
like a model of a histogram
density curves have an area of exactly ____ underneath it
1
median and mean on a density curve?
median- divides area under the curve in 1/2
mean- curve would balance if made of solid material
if a density curve is skewed, the mean line is _____ compared to the median
closer to the tail end (balance point)
Normal curves are what?
They are density curves!
Shape of a normal curve
All normal curves have the same overall shape; symmetric, single-peaked, & bell-shaped
How are normal curves described?
completely described by giving its mean and standard deviation
where is the mean located on a normal curve?
located at the center of the symmetric curve and is the same as the median
How does a normal curves standard deviation affect its spread?
curves with larger standard deviations are more spread out
how are normal distributions abbreviated?
N( mean , standard deviation )
The 68-95-99.7 rule is also called what?
the empirical rule
What does the 68-95-99.7 rule tell us?
in a normal distribution approximately…
68% of the observations fall within 1 standard d. of the mean
95% within 2 s.d. of the mean
99.7% within 3 s.d. of the mean
example of a normal distribution?
height
example of not usually a normal distribution
income (usually right skewed)
in order for data to be normal… what does it have to follow? How do you check for this?
it has to follow to 68-95-99.7 rule
Create a NPP, if it is roughly linear, the data is roughly normal
if something is in the 80th percentile, what does that mean?
80% of the total data is below you
what does it mean to have a z-score of .6126
it means that this value is approximately .6126 standard deviations above the mean
when to use inverse cdf?
When you know the percent below
When to use normal cdf?
when you know the z score and what part of the data youre trying to ifnd
