3-Properties of distributions Flashcards
What is a central tendency?
The summarization of a score distribution by providing a single number. This number is called an average
What are the three most common central tendencies?
Mean, median and mode
What does this symbol (Σ) means?
It means the sum (capital S in greek)
1)What does this formula is used for ?:
m= (Σy)/n
2) What does every letters mean?
1) This formula is to calculate the mean in a sample
2) m: mean
Σy: The sum of all the scores in y : every score
n: The numbers of scores
What are Greek symbols and Roman characters used for respectively?
1) Greek : parameters
2) Roman : statistics
What does this symbol µ means ?
The mean of a population
What is the median ?
A number that seperates an ordered set of number in two groups of equal size
What is the formula to find the median position?
Median position = (n+1)/2
What happen with even numbers of scores for finding the median?
The median position will be between two scores, so we will do the average of those two scores.
What is the mode ?
The most occuring score in a set
What is the main difference between the mean and median?
All scores are used with the mean. If one if removed, it is going to change. In the median, only a few scores is gonna affect it, so if one is removed, it won’t change much.
Between the mean, median and mode, what is the best for qualitative variables ?
The mode
What does dispersion stands for ?
how spread out scores are in a distribution of a quantitative variable
What is an outlier?
A score that is unusually far from the central tendency of the distribution.
True or false. You can exclude outliers with the right justification
True, if the outliers are judged invalid
What are the three most used measures of dispersion?
The range, variance and standard deviation
How do you calculate the range?
Max-min
True or false. The range is highly sensitive to outliers
True
What is the variance ?
The mean squared deviation from the mean
What does this symbol stands for : σ2 (sigma square) ?
The variance (mean squared deviation from the mean)
What is the formula for variance in a POPULATION ?
σ2= S(y-mew)^2/N
so every score in y - mew
What is the deviation score, and what is the formula ?
The difference between a score and the mean
y-mew
What is the formula for variance in a SAMPLE:
s^2= S(y-m)^2/(n-1) or ss/(n=1)
What is the standard variation ?
The square root of the variance
What is the formula for standard variation in POPULATION?
o= squaroot of o^2=squaroot of S(y-mew)^2/N
What does the symbol σ stands for ?
Standard variation
What is the formula for standard deviation in a SAMPLE:
s= squareroot of s^2= squareroot of S(y-m)^2/(n-1)
In words, what does the standard deviation means in a context?
It is roughly the average distance (deviation) of scores from the mean.
What is another formula to calculate the sample variance?
s^2=s^2pop* (n/n-1)
Why is the standard deviation more intuitive than the variance for measuring variability?
because it is more directly related to differences in variability between two sets of scores.
How would you report statistics of mean and standard deviation ?
M=
s=
What does the error bars represents in a graph ?
It represent the variability
What is the shape of a distribution ?
How density (or frequency) changes as a function of the values of the variable.
What is a normal distribution ?
When it is symmetrical with a single peak (mode) (unimodal)
What are non-normal distribution called ?
Skewed distribution
What are right skewed and left skewed also called ?
Right: Positively skewed
Left : Negatively skewed
What is the consequence of left and right skewed ditribution
1) Right : floor effects
2) Left: ceiling effects
With the skew, if the tail goes towards the biggest possible score it is a negative or positive skew
Positive
What is the position of the mean in a positively skewed distribution?
The mean is going to be above the median
What is kurtosis ?
The sharpeness of the peak of a probability distribution
How do you call a normal kurtosis ?
mesokurtic
How do you call a kurtosis with sharp peak ?
leptokurtic
How do you call flat kurtosis?
platykurtic
What are multimodal distributions?
Distributions with more than one peak
