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1

statistics

the science of using an assortment of methods to systematically collect, organize, summarize, analyze, and interpret information

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descriptive statistics

tabular, graphical, or numerical summaries of data for a particular group

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3

statistical inference

using data collected from a sample in order to make estimates and test hypotheses about the characteristics of a larger inference

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4

population

the set of all elements of interest in a particular study

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census

collecting data for the entire population

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sample

subset of the population

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sample survey

collecting data for a sample

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data

information that we collect and analyze

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data set

all of the data that is collected for a study

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elements

the subjects of a study; entities on which data is collected

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variable

attribute of the subjects/elements we are interested in studying

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observation

set of all measurements collected for one subject/element

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total data values

elements x variables

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measurement scale

the nature of the values that are assigned to variables

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nominal

categorical variables; does not indicate ranking (ex. gender, zip code)

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ordinal

ranked data; distance between not equal/known (ex. socioeconomic class, TRACE scale)

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interval

always numeric; distance between integers are equal; no absolute zero (0 doesn’t mean “absence of”) (ex. temperature, dress size)

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ratio

lowest value is always zero; has an absolute zero (0 means “absence of”) (ex. age)

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qualitative

nominal or ordinal; use words (or rank number) to describe subjects/elements

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quantitative

interval or ratio; use numbers to describe subjects/elements

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continuous

variables can take on values between whole numbers (fractions/decimals)

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discrete

usually only take on whole number values (except shoe size)

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experiment

a variable is specifically manipulated by the researcher

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constant

a characteristic of elements/subjects that does not vary from one subject to the next

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control variable

held constant in a research study by observing only one of its levels

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observational research

levels of independent variable already exist (ex. gender, age); cannot make causal statements; looks for relationships between some set of variables

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cross-sectional studies

provide a “snapshot” of different groups at one point in time

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time series studies

longitudinal; use data that are collected on the same subjects/elements over several points in time; observe changes over time

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effects

changes in data patterns

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cyclical effect

any usual/consistent variation in daily, weekly, monthly, or annual data not related to change in season

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seasonal effect

change in data that can be explained by/attributed to annual calendar-related events

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irregular effect

any change in the data is not related to a regular cycle or season; caused by unusual events

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33

business analytics

the use of data, tehcnology and statistical analysis to answer questions

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descriptive analytics

use of data to understand past and current business performance

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predictive analytics

use of historical data to identify patterns or relationships and to make predictions about what will happen in the future

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prescriptive analytics

identify the best alternatives to minimize or maximize some objective

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parameters

greek symbols representing descriptive measure of a population

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38

sample statistics

roman letters representing descriptive measures of a sample

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random sample

each member of population has an equal and independent chance of being included in the sample

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sampling bias

when a sample is collected in a way that results in some members of the population being more or less likely to be included than others

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raw data

data that has not been organized or summarized in any way

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frequency distribution

the list of all frequencies for all categoreis

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relative frequency distribution

the proportion of the observations that belong to a category f/n

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percent frequency distribution

the percent of the observations that belong to a category f/n x 100

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class intervals

data divided into sets with equal widths

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class midpoint

the value half way between the upper and lower limit of an interval

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cumulative frequency distribution

total number of items that have values less than or equal to the upper limit of each class

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data vizualization

the process of displaying data meaningully in order to improve decision-making

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dashboard

visually summarizes key business information

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line charts

display data over time

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pie chart

used to display relative frequency or percentage distributions

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bar chart

used to visually present qualitative data; separated bars

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histograms

display frequency distributions of quantitative variables; no spaces between bars

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frequency polygon

points used to depict frequency for each class interval

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scatter plot

displays relationship between two quantitative variables

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trendline

depicts general direction of the relationship between variables

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positive relationship

as x increases, y increases

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negative relationship

as x increases, y decreases

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symmetrical distribution

similar on both sides

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negatively skewed distribution

skewed left; most data fall at upper end

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positively skewed distribution

skewed right; most data fall at lower end

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skewness

the measure of the symmetry of a data distribution

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kurtosis

the measure of how peaked or flat a data distribution is relative to a normal distribution

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excess kurtosis

kurtosis - 3

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mesokurtic

kurtosis = 3, excess = 0

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leptokurtic

kurtosis > 3, excess > 0

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platykurtic

kurtosis < 3, excess <0

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mildly skewed rule of thumb

skewness between -.5 and +.5

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moderately skewed rule of thumb

skewness between -.5 and -1 or between +.5 and =1

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highly skewed rule of thumb

skewness less than -1 or greater than +1

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standard error calculation

plus or minus 3 times the standard error of skewness

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mode

value with highest frequency of occurance; unaffected by outliers

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median

the middlemost value when arranged in ascending order; not affected by outliers

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median index

(n+1)/2

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mean

best measure for normal data; can be pulled in direction of outliers

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positive skew central tendencies

mode < Median < mean

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negative skew central tendencies

mean < median < mode

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mean of the means

if groups are the same size use ___

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79

weighted mean

used to calculate the mean of two or more groups when their sample sizes are not equal

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percentiles

divide rank-ordered data into 100 equal parts

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quartiles

divide rank-ordered data into 4 equal parts

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measures of variability

describe the spread of the data around the center

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range

largest value - smallest value; sensitive to outliers

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Interquartile Range

Q3-Q1; middle half of data

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box and whisker plot

shows the center, the spread, and outliers of a data distribution

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five number summary

smallest value(within inner fences), Q1, Q2, Q3, largest value(within inner fences)

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inner fences

Q1 - (1.5 x IQR) Q3 + (1.5 x IQR)

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outer fences

Q1 - (3 x IQR) Q3 + (3 x IQR)

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middle 50% of data positively skewed

if median in box is on the left side; the ___

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outer 50% of data positively skewed

if longest whisker is to the right of the box; the ___

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deviation score

the distance from any score in teh data to the mean of the distribution

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zero

deviation scores add up to ___

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sum of squares

sum of squared deviation scores ; total variation in the data set

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population variance

sum of squares divided by N; average variability

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sample variance

sum of squares divided by n-1; average variability

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standard deviation

square root of variance; average deviation around the mean of a distribution

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degrees of freedom

the number of scores that are free to vary

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empirical rule

applies to normal data; 68% between 1 standard deviation, 95% between 2 standard deviation, 99.7% between 3 standard deviation

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chebyshev’s theorem

any data set (skewed); what percentage of data lie within k standard deviations of the mean (k>1)

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coefficient of variation

how large the standard deviation is relative to the mean

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