Statistics 1 Flashcards by Enikö Maria Petrak

What does it mean if a variable has a nominal scale?

Consists of numbers/ categories, cannot be put into a logical order, has no fixed unit of meaurement

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What does it mean if a variable has a ordinal scale?

Consists of numbers/ categories, can be put into a logical order, doesn’t have a fixed unit of measurement

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What does a variable with a interval scale have?

consists for numbers, can be put into a logical order, has a fixed unit of measurement, 0 has no real meaning

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What does it mean if a variable has a ratio scale?

Consists of numbers, can be put into a logical order, fixed unit of measurement, meaningful 0 point

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Name 3 example for a nominal scale.

Which party do you lean towards? What hair color do you have? What fruits do you like? … etc.

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Name 3 examples for a ordinal scale.

How often have you felt angry? Who performed best in the exam? Placements of a race. …etc.

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Name 3 examples for a interval scale.

How satisfied are you with…? Rank year of birth… . Temperature Celsius/ Farenheit… . Etc.

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Name 3 ratio scales.

Height in cm. Monthly income in Euro. Weight in kgs. …etc.

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What scale is it: categories/ words, no order, no fixed unit of measurement

Nominal scale

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What scale is it: categories/ words, logical order, no fixed unit of measurement

Ordinal scale

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What scale is it: numbers, order possible, fixed unit of measurement, 0 has no real meaning

Interval scale

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What scale is it: numbers, orders possible, fixed unit of measurement, meaningful 0 point

Ratio scale

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What are the three measures of central tendency?

Mean, Median, Mode

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What is the mean?

Sum of all values divided by total number of values

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What are disadvantages of the Mean?

Can be distorted by extreme values

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What is the Median?

Central value of a dataset

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How do you find the median?

Put values in order, find the middle. Even amount of values: amount of values plus one, divided by 2

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Advantages of the mean

Not distorted by „extreme values/ outliers“

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When is the effect of extreme values larger?

In small datasets

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What’s the mode?

Category which occurs most often

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What’s the mode also called?

Modal value

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Which measure of central tendency is important for nominal data?

Mode

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How many values can median and mean have?

One

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What are three measures of dispersion?

Range, IQR, standard deviation (and variance)

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What’s the range?

Distance between lowest and highest value

What’s the simplest way of showing the variability?

Range

How do you calculate the range?

Maximum minus minimum

What’s a disadvantage of the range?

For example: two datasets with completely different distributions that have the same minimum and maximum have the same range

How do you find the interquartile range?

Divide the dataset into 4 equal parts (Q1, Q2, Q3)

What’s Q2 in the IQR?

The median

What’s the standard deviation and variance?

Mean of all squared deviations in the dataset

What’s the deviation

Amount by which a value differs from the mean

What are the 6 steps to calculate the standard deviation?

1. Find the mean 2. Find the distance of each value from the mean 3. Square the deviations 4. Sum up all squared deviations 5. Divide by N 6. Take the square root of the result

How do you interpret the standard deviation?

„On average a value deviates by ____ from the mean.“

When is it possible to compare standard deviations from different datasets?

Only possible to compare IF a) both datasets have same number of obervations AND b) if they have same unit of measurement

Whats the CV?

Coefficient of variation

How do you calculate the CV?

Standard deviation divided by the mean

Whats the rule of thumb?

CV > 1 = rather high variability, CV < 1 = rather low variability

When should the CV only be used?

Only used for ratio-level data, NOT for interval-level data

Name graphical represantation of data

bar charts, line charts, histogram, box-plot

What do graphs need to be?

easily understandable and clearly labelled, need to show more than the obvious

Why do bar charts have to start at 0?

Graphs not starting at 0 can be misleading

What are line charts used for?

time series data (e.g. months, years, days etc.), best used for comparisons over time and between entities

What does a Histogram do?

shows pattern of the whole dataset

what are the three properties of histograms?

1. height of the collum is proportional to the number of observations 2. all intervals are displayed, even if there are no observations 3. collum are equally wide ("bin width")

What does the box-plot do?

shows information on typical value and the spread in one graph

what informations does the box-plot combine?

Minimum and Maximum (without outliers), Q1, Median, Q3

What are out outliers?

values equal or bigger than Q3+1,5*IQR or values equal or smaller than Q1-1,5*IQR

What are far out outliers?

Values equal or bigger than Q3+3*IQR or values equal or smaller than Q1-3*IQR

What are frequency distributions used for?

for larger datasets (30 and higher) we can look at overall distribution

Why are frequency distributions used for larger datasets?

with larger datasets we have enough repetitions of the same or similar values

What are the steps to make a frequency table?

1. Make a list with all values in your dataset starting with the lowest 2. Go through your scores and count the number of values for each of the values in your dataset 3. Calculate the percentage of scores for each value 1-10

What do frequency tables or histograms describe?

frequency distribution (show how frequencies are spread out)

What does frequency distribution show?

pattern of frequencies over the various values

What are the shapes of distribution?

unimodal distribution, bimodal distribution, multimodel distribution and rectangular distribution

How to differenciate the shapes of distribution?

unimodal: 1 peak bimodal: 2 peaks multimodal: three or more peaks rectangular: all values have same frequency

What frequency distribution more likely in real life data?

unimodal distributions, bimodal and multimodal less often

What are the properties of symmetrical distributions?

1. two halfs look the same 2. equal number of causes on each side 3. typical value lies in the middle

Whats the opposite of symmetrical distribution?

Skewness (=Schiefe)

What types of skewed distribution are there?

- distribution skewed to the left (negatively skewed) - distribution skewed to the right (positively skewed)

Whats the "floor effect"?

a lot of values (in lower boundaries) can be found in the lowest interval

What are examples of lower boundaries?

-cant buy groceries with less than 0€ - parents cant have less than 0 children

What are examples of upper boundaries?

- number of cinema tickets sold (limit is capacity of theatre) - percentage of correct answers in mutliple-choice test (max 100%)

Statistics 1 Flashcards

(63 cards)