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acronym to describe a distribution

SOCS

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Socs

spread; state the highest and lowest value

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sOcs

outliers; state values that stand out

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soCs

center; approximate mean

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socS

shape; symmetry or skewedness

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symmetric

mean = median

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skewed left

mean < median

negative skew

mean to the left of median

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skewed right

mean > median

positive skew

mean to the right of the median

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time plot of a variable

plots each observation against the time at which it was measured

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5# Summary

minimum, Q1, median, Q3, maximum

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IQR

the distance between the first and third quartile

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IQR =

Q3 - Q1

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calculate lower outlier

Q1 - 1.5(IQR)

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calculate higher outlier

Q3 + 1.5(IQR)

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second method to calculate outliers

if value is located 2 or more SD’s above or below the mean

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standard deviation

average distance from the mean of all the values in a data set

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SD for a population

SD = sqrt [ Σ ( x - μ )² / N ]

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SD for a sample

SD = sqrt [ Σ(x - x̄)² / (n - 1) ]

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frequency table

gives the number of cases falling into each category

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relative frequency table

gives the proportion of cases falling into each category

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percentages, relative frequencies, and rates all provide the same information as

proportions

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bar charts(graphs) are used to display

frequencies for categorical data

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discrete variable

can take a countable number of values, could be finite or countably infinite

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continuous variable

can take on infinitely many values but values cannot be counted no matter how small the interval there is, there is always a value in between

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univariate

one main peak

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bimodal

two prominent peaks

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uniform

height is the same

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gap

region between two values with on data observed

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cluster

concentration of data separated by gaps

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statistic

numerical summary of sample data

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p^th percentile

value that has p% of data less than or equal to it

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variability

how spread out scores are in a distribution

The degree to which data points differ from each other or from the mean value. It can be measured by calculating the variance or standard deviation of a dataset.

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3 measures of variability

range, IQR, SD

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the empirical rule

This rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

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