PS296 Study Guide - Midterm Guide: Normal Distribution, Central Limit Theorem, Standard Deviation
Normal Distributions:
-distribution that forms symmetrical, unimodal, asymptoptic (tails never touch x value) bell
curve
-mean median mode located at midpoint of curve and shape is defined by mean and SD
-total area under the curve equals 1 (divided into 4 percentiles)
-vertical/Y axis = density, frequency of scores at each value
-horizontal/X axis = value of scores
-as sample size increases, shape of curve becomes more normal, only works when samples
are randomly drawn from the population (central limit theorem)
The Standard Normal Distribution:
-mean of 0, standard deviation of 1
-area under curve represents probabilities/proportions and total 1.00 or 100%
-standardization is process of transforming normal scores into standard normal distribution /
x (raw) scores into z (standard) scores
-positive z scores are greater than 0 and on right side of curve
-most scores are between 0 and 3 standard deviation units
-mean to z = how far away the value is from the mean
-percentile/cumulative percent: the point below which a specified percentage of scores fall
Emprical Rule (for symmetrical, bell shaped distribution)
-68% of the data lie w/i 1 standard deviation of the mean (z = 1, mean to z x2 = .6826)
Document Summary
Distribution that forms symmetrical, unimodal, asymptoptic (tails never touch x value) bell curve. Mean median mode located at midpoint of curve and shape is defined by mean and sd. Total area under the curve equals 1 (divided into 4 percentiles) Vertical/y axis = density, frequency of scores at each value. As sample size increases, shape of curve becomes more normal, only works when samples are randomly drawn from the population (central limit theorem) Area under curve represents probabilities/proportions and total 1. 00 or 100% Standardization is process of transforming normal scores into standard normal distribution / x (raw) scores into z (standard) scores. Positive z scores are greater than 0 and on right side of curve. Most scores are between 0 and 3 standard deviation units. Mean to z = how far away the value is from the mean. Percentile/cumulative percent: the point below which a specified percentage of scores fall.
