Dit document bevat een samenvatting van Hoofdstuk 1 t/m 4 en 6 t/m 12 uit het boek Managerial Statistics van Keller (2014). De samenvatting bevat alle theorie die je moet weten voor het tentamen van Statistiek. Statistiek is onderdeel van de premaster, RSM Erasmus Universiteit. De samenvatting is i...
Chapter 1 – What is statistics?
- Statistics = is a way to get information from data
- Descriptive Statistics: summarizing and presenting data in effective way.
- Inferential Statistics: drawing conclusions about population based on sample data
- Key statistical concepts
Population = group of all items of interest to a statistics practitioner
Parameter is the descriptive measure of the population
Sample = set of data drawn from the studied population
Statistic is the descriptive measure of sample
Statistical inference = the process of making an estimate, prediction or decision about a
population based on sample data – two measures of reliability
Confidence level: proportion of times that an estimating procedure will be correct
Significance level: how frequently the conclusion will be wrong
Chapter 2 – Graphical Descriptive Techniques I
- Types of data and information
Variable = characteristic of a population or sample
Values = possible observations of the variable
Data = observed values of the variable (datum is singular)
- Four types of data
Ratio = highest level, absolute point of zero - quantitative
All calculations allowed: = ≠ < > + - * / often average calculated
Interval = numbers such as heights, weights or incomes – quantitative & numerical
Ordinal = categories where order of values have meaning – ranking = ≠ < >
No specific graphical technique: bar charts and pie charts can be used
Nominal = categories such as single, married or divorced – qualitative & categorical
Can only count frequency or percentage of occurrence (relative frequency): = ≠
Frequency distribution presented in bar chart or pie chart (proportions)
- Higher-level data may be treated as lower-level data but not the other way around
Chapter 3 – Graphical Descriptive Techniques II
- Histogram is used for interval data
Observations that fall into a series of intervals are classes
Intervals don’t overlap, every observation is assigned and the intervals are equally wide
- Number of classes is based on the number of observations: # = 1 + 3.3log(n)
- With of class = (largest observation – smallest observation) / number of classes
- Shapes of a histogram
Symmetric: two sides identical in shape and size
Skewness: long tail extending to right (positively skewed \) or left (negatively skewed /)
Modal class: class with the largest number of observations
Unimodal histogram: has only one peak – bimodal histogram: has two peaks
Bell Shape: a special type of symmetric unimodal histogram
- Stam-and-leaf display is similar a display as histogram but with actual observations
- Relative frequency distribution is created by dividing frequencies by number of observations
, Total sum is always 1.0/100%
Cumulative relative frequency distribution highlights observations below class limits
Ogive is graphical representation of cumulative relative frequencies
Chapter 4 – Numerical descriptive techniques
- Measures of central location – three different measures
Mean: μ = the average - only for interval and ratio data (formula sheet)
Median = middle observations when placing all in order
Not as sensitive to extreme values as the mean
Best for either very small or extreme number of observations (ordinal, ratio, interval)
Mode = observation that occurs with the greatest frequency
For populations and large samples report modal class
- Measures of variability – spread of variability (only for interval and ratio data)
Range = largest observation – smallest observation
Variance: σ² (population) and s² (sample) – (formula sheet)
Standard deviation: σ and s = related measure
Mean absolute deviation (MAD) is average absolute value
Standard Deviation: σ = √σ² and s = √s²
- Empirical Rule can be used when histogram is bell shaped
68% of all observations fall within one standard deviation of the mean
95% of all observations fall within two standard deviations of the mean
99.7% of all observations fall within three standard deviations of the mean
- Chebysheff’s Theorem applies to all shaped of histograms: 1-(1/k²) for k>1
- Coefficient of Variation: CV = σ / μ and cv = s / x
Chapter 6 – Probability
- Probability provides a link between population and sample
- Random experiment = action/process that leads to one of several possible outcomes
Example: flip a coin – either head or tail of grade on test – A, B, C, D or F
List of outcomes includes all possibilities, and no two outcomes can occur twice
Sample space: S = list of all possible outcomes – exhaustive and mutually exclusive
- Two requirements of probabilities – given sample space S = {O 1, O2, …., Ok}
Probability outcome between 0 and 1: 0 ≤ P(Oi) ≤ 1 for each i
Sum of all probabilities is 1
- Classical approach: calculate games of chance – head or tail is 50%
- Relative frequency approach: long-run relative frequency, look at past – 200 out of 1000 is 20%
This method is always used to interpret the probability
- Subjective approach: define probability as degree of belief – analysing factors influencing stock
- Event = collection/set of one or more individual outcomes in a sample space
- Probability of an event = sum of probabilities of simple event that make the event
- Intersection of Events A and B: event that occurs when both A and B occur – A and B
Probability of the intersection = joined probability
- Marginal probabilities: adding the probability across rows or down columns
- Conditional probability: probability of A given event B – P(A|B) = P(A and B) / P (B)
- Union of Events A and B: event that occurs when either A or B or both occur – A or B
- Probability rules
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