Exam grade: 9.1 Complete notes from all Introduction to Statistics lectures with all pictures from slides, with nice aesthetics and a beautiful purple layout. I got a high grade from an exam so I guess the notes are helpful :)
● How do we draw conclusions about a population from a sample?
● Key concepts: probability, empirical rule, sample, population, sampling
distribution, standard error, confidence interval, central limit theorem,
➢ Types of variables
○ different types of variables require different types of description
➢ Core function of statistics is to describe data
○ Centrality: mode, median, mean
■ The type of variable defines the centrality measure that we can use
■ Mean for the dichotomous variable equals proportion
● The proportion is basically the same as the percentage
○ Dispersion: Standard deviation
■ The sum of all squared distances to the mean.
● If all observations are clustered around the mean, the sum of
distances will be small.
● If observations are widely dispersed around the mean, the
sum of distances will be larger.
■ It’s a summary measure of the average distance to the mean.
■ If there is more dispersion, the standard deviations will be higher.
, ➢ Comparing distributions - z-scores
○ z-score: number of standard deviations from the mean
○ z-scores take into account differences in both centrality and dispersion
○ z-scores are a key concept in inferential statistics
○ z-scores help us to describe bell-shaped distributions
■ normal distributions - bell-shaped and symmetrical
Distributions of data
➢ Bell-shaped distributions (perfectly symmetrical around the mean ӯ)
○ we can describe it with empirical rule
○ 68% of all observation within 1 standard deviation from mean (between ӯ-sand ӯ+s)
○ 95,4% of all observations is between 2 standard deviations from mean (between
ӯ-2s and ӯ+2s)
○ 99,7% within 3 standard deviations (between ӯ-3s and ӯ+3s)
➢ we can apply empirical rule to all normal distributions
➢ frequency distributions
○ a listing of possible values for a variable, together with the number of
observations at each value
Probabilities and probability distributions
We can think of frequency distributions as probability distributions as well.
➢ provide probabilities for all the possible outcomes of a variable, lists the possible
outcomes and their probabilities
➢ I pick one random respondent that was sampled:
, ○ What is the probability that he/she/them is older than 20?
○ What is the probability that he/she/them studies more than 20 hours?
➢ We can determine this on the basis of the distribution!
➢ Probability = p
○ The probability is the area under the curve.
○ Each area under a bell-shaped curve can be expressed in a probability p
Standard normal distribution
➢ theoretical distribution used in inferential statistics
○ we use the standard normal distribution for calculations
○ bell-shaped and perfectly symmetrical
○ mean (ӯ) = 0, standard deviation (s) = 1
○ we can apply empirical rule here, too
➢ Probabilities can be defined as z-scores
■ in the standard normal distribution z = yi
➢ Every position in a normal distribution has a z-score with a corresponding probability.
○ Can be found in Table A.
○ For normally distributed variables we can convert z-scores to probabilities
(and the other way around)
Example using the table A
Voordelen van het kopen van samenvattingen bij Stuvia op een rij:
Verzekerd van kwaliteit door reviews
Stuvia-klanten hebben meer dan 700.000 samenvattingen beoordeeld. Zo weet je zeker dat je de beste documenten koopt!
Snel en makkelijk kopen
Je betaalt supersnel en eenmalig met iDeal, creditcard of Stuvia-tegoed voor de samenvatting. Zonder lidmaatschap.
Focus op de essentie
Samenvattingen worden geschreven voor en door anderen. Daarom zijn de samenvattingen altijd betrouwbaar en actueel. Zo kom je snel tot de kern!
Veelgestelde vragen
Wat krijg ik als ik dit document koop?
Je krijgt een PDF, die direct beschikbaar is na je aankoop. Het gekochte document is altijd, overal en oneindig toegankelijk via je profiel.
Tevredenheidsgarantie: hoe werkt dat?
Onze tevredenheidsgarantie zorgt ervoor dat je altijd een studiedocument vindt dat goed bij je past. Je vult een formulier in en onze klantenservice regelt de rest.
Van wie koop ik deze samenvatting?
Stuvia is een marktplaats, je koop dit document dus niet van ons, maar van verkoper juliaradzieta. Stuvia faciliteert de betaling aan de verkoper.
Zit ik meteen vast aan een abonnement?
Nee, je koopt alleen deze samenvatting voor €5,48. Je zit daarna nergens aan vast.
