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Level 37

Mean-Standard Deviation Portfolio Theory


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Standard Deviation
An estimate of the average variability (spread) of a set of data
Standard Error of the Mean
The standard deviation of the sampling distribution of a statistic (the mean)
Standard Error of Measurement
Standard deviation of a persons' repeated test scores; inversely related to reliability (ex. reliability = 1.0, SEM = 0); helps you figure out what will probably happen if the subject takes the same test again
population proportion
pi (π)
population mean
mu (µ)
population standard deviation
lower case sigma (σ)
sample proportion
p-hat (p̂)
sample mean
x-bar (x̄)
s
sample standard deviation
Observational Study
Attempts to collect information and draw conclusions about a population of interest without influencing the results.
Experiment
Attempts to find cause-effect relationships by imposing some kind of treatment on the experimental units.
Bias
The study systematically favors a certain conclusion.
Sampling Bias
Bias that is connected to the sampling process. For example: If the selection comes from people who have phones, those without phones may tend to respond differently. They are under represented.
Non-Sampling Bias
Bias related to the process of gathering information from the selected sample.
Natural Variation
Inherent deviation between the sample result and the population.
Anecdotal
The use of personal experience or one counter example to a widely accepted conclusion in order to debunk.
Median
The point of equal area
Mean
The point where if the figure were made of solid material the weight would be even.
Percentile
The proportion of data or the curve that is below a given value.
Confidence Intervals
Attempt to capture a value that describes the population based on a sample value called a statistic.
n
sample size
μ
Mu, population mean
σ
population standard deviation (lower case sigma)
S^2
sample variance
σ^2
population variance
p^
sample proportion
p
population proportion
mode
value that appears the most
Range
is the highest score minus the lowest score (some exams will add 1 to the answer). e.g., 24, 46, 3, 26, 47. 47 - 24 = 23 + 1 = 24
variance
(Σ(x-xbar)^2)/(n-1)
correlation
the extent to which variables are related
High Standard Deviation
The data are widely spread
Error Bars
Graphical representation of the variability of data
68%
±1 of Standard Deviation
95%
±2 of Standard Deviation
t-Test
A test used to find out whether there is a significant difference between the means of two populations
Q1
median of the lower 50 percent of ranked data
Q3
median of the upper 50 percent of ranked data
IQR
measure of variability that represents the range of the middle half of the data
ΣX^2
The symbol for the sum of the squared Xs
(ΣX)^2
The symbol for the squared sum of X
S^2X
The symbol for sample variance
SX
The symbol of sample standard deviation
σ^2x
The symbol used when describing the true population variability
s2X
The symbol used to estimate the variability in the population
biased estimator
A formula for a sample's variability that invalid dividing by N is biased toward underestimating the corresponding population variability
degrees of freedom
The number of scores in a sample that are free to vary, and thus the number that is used to calculate an estimate of the population variability; symbolized by df
estimated population standard deviation
The unbiased estimate of the population standard deviation calculated from sample data using degrees of freedom (N-1)
measure of variability
Measures that summarize the extent to which scores in a distribution differ from one another
population variance
The average squared deviation of scores around the population mean
proportion of variance accounted for
The proportion of the error in predicting scores that is eliminated when, instead of using the mean of Y, we use the relationship with the X variable to predict Y scores; the proportional improvemen…
sample standard deviation
The square root of the sample variance or the square root of the average squared deviation of sample scores around the sample mean
sample variance
The average squared deviation of a sample of scores around the sample mean
sum of the squared Xs
A result calculated by squaring each score in a sample and adding the squared scores
unbiased estimator
A formula for a sample's variability that involves dividing by N-1 that equally often under- and over-estimate the corresponding population variability