Task 2 Flashcards by Anna Eiser

Which 2 main types of data are there?

Categorical data

Quantitative data

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Which 2 categories of categorical data do you know?

Nominal (naming)

Ordinal (ordering)

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Which type of categories does nominal data have?

Name an example

Equal categories (without order) 
gender: male/female

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Which type of categories does ordinal data have?

Name an example

ordern categories (with order) 
education level (low/ middle / high)

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By using categorical data, are the distances on scale meaningful?

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Which suitable table do you use for categorical data?

frequency table

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Which suitable graphs do you use for nominal data?
What are classical representations?
Name 2

Pie chart

Bar chart

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Which suitable measure of central tendency do you use for nominal data?

mode

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Which suitable measures of central tendency do you use for ordinal data?

Mode

Median

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Which suitable measure of central tendency do you use for quantitative data (interval & ratio) ?

Mode
Median
Mean

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Is there a suitable measure of dispersion for categorical data?

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Which suitable measures of dispersion (Verteilung) do you use for quantitative data?

Interquartile range (IQR)
Standard deviation

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Name 2 main data scores which are used by quantitative data

Interval (distance)

Ratio (rate)

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Which suitable table do you use for quantitative data?

Stem and leaf plot

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Which suitable graph do you use for quantitative data?

Name 2 classical representations

Histogram

boxplot

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What do you know about the distance between the variables by using interval? Example

Meaningful numbers, for instance IQ (50-150)

The distance between consecutive units is always equally large

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What do you know about ratio

an interval variable with an absolutions zero point, for instance age

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When do you use a stem and leaf plot?

if you have a low number of recordings

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What are the advantages of a histogram?

easy to represent many data points

easy to interpret data roughly (ungefähr)

Which are the 3 special interest points of a histogram?

Extreme values (outliers) 
Number of peaks (modes) 
Symmetry

When do you use the box-plot?

visual representation of large data set
fast recognition of outliers
easy comparison of several groups

Name 4 Middle values / suitable measures of central tendency

mean
median
mode
IQR

Mean

Definition?
Calculation?
How to deal with Outliers?
Example

• Average value / the scores center of mass
• Calculation: adding all values, dividing sum by total numbers of observations
• Sensitive to outliers
(be careful using it in case of skewed distributions or outliers)

Example:
1-3-3-4-9
Sum=20
Mean= 20/5= 4

Usage of mean

for quantitive data (interval variables and up)

tells you something about the frequency, order and value of scores

Median Definition? Determing? How to deal with outliers? Example

* Middle value (50% lies below and 50% above) * Determining: ordering all values from small to large and picking the middle (N+1):2 * Robust towards outliers Example: 1-2-4-4-5 • Median: 4

Usage of median

okay for ordinal variables and up (interval and ratio) | tells you some thing about the frequency and order of scores

Mode Definition? Determing? How to deal with outliers? Example

* Highest frequency of value * Determining: which value or category appears most frequent / often * Robust towards outliers Example: 1-2-2-4-12 • Mode: 2

usage of mode

is always okay | tells you something about the frequency of scores

deutsches Wort für distribution

Verteilung

deutsches Wort für skewed

verzerrt

What is a Z-score?

* A standardized measure of standard deviations. * Example: if SD=15 and a person has a score 15 points above the mean his Z-score= +1 * Measures how many standard deviations an observed value differs from the mean * Does not change shape of distribution * Measure of center and spread might change

What is the Standard deviation

the average deviation from the mean | the squared value of this is called the variance

How do you calculate the standard deviation?

take the difference of each score from the mean, square these difference, sum them up, divide them by the total amount of scores minus 1 and take the square rout of the outcome

Usage of standard deviation

okay for quantitative data (interval variables) | is not resistant to outliers

Interquartile range IQR

the range between which the 50% middle scores fall IQR= Q3-Q1 for interval variables

Five-number-summary

five quantities in a row which summaries the complete distribution minimum-Q1(25%)-median-Q3(75%)-maximum

1,5* IQR criterion

to identify a score as an outlier downward outlier: Q1-(1,5*IQR) is the score even lower than this outcome, we consider it as an outlier upward outlier: Q3+(1,5*IQR) if a score is even higher than this outcome, we say its an outlier indeed

centring

shift all scores such that the mean becomes 0 C=X-mean the shape of the distribution gets not effected at all; the only thing that changes is the mean

Standardising

shift all the scores such that the mean becomes 0, and then change the scores such that the standard deviation becomes 1 as well (Z-formula)

Multiplying

multiply all scores by a certain number | X´= a*X

What is the difference between a histogram and a bar graph?

A bar graph presents different groups (categorical data), a bar graph has space between its bars

Can the variance be negative? Explain

no it can't because its the standard deviation im Quadra

if you have a normal distribution how much percent does Z1 include?

68%

If you have a normal distribution how much percent does Z2 include

95%

If you have a normal distribution how much does Z3 include?

99%