3: Numerical Descriptive Measures Flashcards
How do you calculate the mean?
Sum of observations divided by number of observations
How do you calculate the median?
The middle value if an odd number of observations.
If even, taking the average of the middle two values.
Why is the median more useful than the mean?
Gives a better representation of the midpoint because the average can be skewed by outliers.
What is the mode?
The most common value in the data set
If data is positively skewed, what is typically the relationship between the mean and median?
If the median is lower than the mean, the histogram will appear to be leaning left, meaning it is positively skewed.
How do you draw a boxplot?
- Find the median, Q1, Q3 and draw the box on the diagram.
- Draw the min and max on the diagram given they are within 1.5 * IQR of Q1/Q3.
- If there is a score outside of the bounds above, mark it with an astrix and plot the first point which appears within the 1.5*IQR.
What is a percentile?
A reflection of where an observation is in a cohort.
85th percentile = 85 ATAR.
What is mean absolute deviation?
This is the sum of the observations from the mean divided by the number of observations.
This tells the average distance from the mean to give a reflection of dispersion.
How do you calculate standard deviation and variance?
Variance is found by the sum of squares of difference from the mean, divided by the number of observations.
StDev is the square root of this.
StDev is in the same unit scale as the observations which is why it is used over variance.
What is coefficient of variation?
This is the standard deviation of the population or sample divided by the number of observations.
What is the sharpe ratio?
This reflects the extra reward per unit of risk.
Calculated by the mean return minus the risk free rate, all divided by the standard deviation of the observation.
Higher the sharpe ratio, the better.
What is Chebyshev’s theorem?
For any kind of data set, the proportion of observations that lie within k standard deviations from the mean is at least 1 - 1/k^2.
So if k = 2, expected that 75% of observations are contained.
What is the empirical rule with standard deviation?
When considering a symmetric, bell-shaped distribution.
68% of obvs are within 1s.
95% within 2s.
99.73% within 3s.
