Week Three Flashcards
(22 cards)
How do you calculate Skewness?
Average cubed deviation from the mean divided by the SD cubed.
What are the attributes of the normal distribution?
- it is symmetrical
- the medium is the point directly under the peak
- mean = 0
- Skewness = 0
- Excess kurtosis = 0
- kurtosis = 3
What is positive Skewness?
When the data is skewed to the right. The value of the mean is the highest, then the median, then the mode.
ME MED MO
What is negative Skewness?
Where the data is skewed to the left. The value of the mode is the highest, then the median, then the mean.
MO MED ME
What is Pearson’s coefficient?
A similar way of measuring Skewness. We need to know the value of the median, the mean and he SD to calculate. It measures two continuous variables.
How do you calculate Pearson’s coefficient?
(mean-median)3 ➗ SD
What is kurtosis?
A measure that tells us if the distribution is more or less peaked than normal.
What are the two types of kurtosis? And what do they mean?
Platykurtic - thinner tails than a normal distribution. Short and fat.
Leptokurtic - fatter tails than a normal distribution, tall and skinny.
What is standardisation?
It is a way of examining whether a variable is normally distributed, it helps us to be able to describe the variable in terms of units of SD.
We standardise so that we can calculate the probabilities associated with a particular value of the variable within a population.
How do you standardise a variable?
Subtract the value for each observation from the mean of the variables.
Then divide by the SD to calculate z.
What does z-score = 0 mean?
The observation equals the mean.
What does z-score = 1 mean?
The observation have a value one standard deviation above the mean.
What are the probabilities associated with the normally distributed variable when we standardise?
- probability of getting a score > than the mean = 0.5 or 50%
- probability of getting a score > 1SD above the mean = 0.159 or 15.9%
- probability of getting a score > 2SD above the mean = 0.023 or 2%
- probability of getting a score > 3SD above the mean = 0.001 or 0.1%
What % of the area does 1.645 SD either side of the mean cover?
90%
What % of the area does 1.96 SD either side of the mean cover?
95%
What % of the area does 2.58 SD either side of the mean cover?
99%
How to we get the sampling distribution of the mean?
By taking lots of samples from the population.
What happens to the shape of the sampling distribution of the mean as sample size increases?
Regardless of the shape of the population it will approach a normal distribution.
What does the location of the normal distribution depend on?
The value of the mean and the standard deviation.
What do the mean and SD determine with the normal distribution?
- Mean: determines the location of the centre of the graph.
- SD: determines the height and the width of the graph.
What happens to the distribution is the SD is:
A. Small?
B. Large?
A. The density function reaches a sharpe peak and becomes Leptokurtic.
B. The density function is flat and low, but still bell shaped and become Platykurtic.
What is the value of the area under the density curve and above the x-axis?
It always equals 1
