unit 2

pth percentile

value with p% of observations less than it

how to calculate a percentile from raw data

count number of values below number youre looking it and put it over the total (if youre looking at 2 of the same values count everything below both of those values)

cumulative relative frequency graph/ogive

used to graph percentiles where y-axis is percentile and x is the variable being measured

what does (50,0.25) mean on a cumulative relative frequency graph?

25% of _____ has a value less than 50 ______

what does adding/subtracting affect vs not affect for data

affects:

• center (mean, median)

• location (quartiles/percentiles)

doesnt affect:
- shape

• spread (range, IQR, S_x)

what does multiplying/dividing affect for data?

affects:

• center (mean, median)

• location (quartiles, percentiles)

• spread (range, IQR, S_x) — but only by absolve value of factor

doesn’t affect:

• shape of distribution

z-score

measures how many standard deviations a specific point is away from the mean (pos = above mean, neg below mean and 0 is the mean)

z-score formula

what is the z-score basically doing

puts data into a universal scale so you can cross-reference unrelated things; talks about relative position

density curve

area under represents all possible sample outcomes; tells you probability that a random sample from a distribution will fall in that range

density curve requirements

• on or above horizontal axis

• area under curve = 1

measurements of center with density curve

• median: splits area under curve in half (50th percentile)

• mean: balance point where curve would balance if made of solid material

normal distribution/normal curve requirements

• symmetric

• unimodal

• bell shape

N(mu, o)

mu = mean; center of curve

o = S_x; distance from center to inflection point

68-95-99.7 rule

• 68% of observations are within 1 S_x from mean

• 95% of observations are within 2 S_x from mean

• 99.7% of observations are within 3 S_x from mean

• same thing applied to z scores but mean is 0 and standard deviation = 1

p (z < x) means

probability of z being below x

finding area/probability from a value

1. draw normal curve with mean, standard deviation, boundary values, shaded ROI

2. use normalcdf and write commands

normalcdf is for

FINDING AREA

finding values from area/probability

1. draw normal curve w/ mean, standard deviation, shaded ROI, and unknown x-value

2. use invNorm to back-calculate x-value

3. convert x-value into an unstanderdized number if its a z-score

use invNorm for

FINDING VALUE FROM AREA

when you calculate probability from z-score

IT ONLY CALCULATES AREA LEFT OF IT (think integration); SO YOU HAVE TO BE CAREFUL OF MANIPULATING MATH TO GET THE AREA YOU WANT

ALWAYSALWAYSALWAYS

include your units AND write a contextualizing sentence for every answer

normal probability plots

• points close to straight line = normal distribution

• systemic deviations = non-normal

• outliers are pts far away from pattern (may or may not signal non-normal distribution)

distribution CANT be normal if

upper bound/lower bound is too close to the mean because that means curve is cut off and skewed

• mean value doesnt have to be 3S_x away from mean because it depends on sample sizes

area of standard deviation boundary things on normal curve

34, 13.5, 2.35, 0.15

concave down indicates right skew when

x-axis has data and y-axis has z-score

concave down indicates left skew when

x-axis has z-score and y-axis has data