Measures of variability Flashcards
Measures of central tendency
Summarises a data set with a single value that is representative of the data set
What has to happen for data to be approximately equal?
The mean, median and mode will all be the same
What is variability
- The extent to which things are not all the same
- How scores differ from one another
The two major roles of variability?
- Inferential statistics
2. Descriptive statistics
Inferential statistics
The amount of variability affects the kind of statements we can make about our population and the degree of confidence we can have in those statements
Descriptive statistics
Variability is an interesting property of a data set in itself - trying to understand the data itself
Low variability
The shape of the distribution is low so a lot of the values cluster around the narrow peak, not a lot of spread
High variability
Much broader tail, more scores distributed over the data set
Numerical measurements of variability - The range
Largest score minus the smallest score - all values can be found within this range - but not very accurate
Possibility for making the range more accurate
- Look at the difference of each score in the distribution from the mean
- Add the differences up and divide by the number of the scores to get the mean deviation
The mean deviation
(xi - x) / n - mean deviation
Mean deviation always sums to 0
Numerical measurements of variability - the variance (s2)
(xi - x)2 / n - The sum of the squared deviation from the mean deviation by the number of scores
Measure of variability in the original units of measurement - standard deviation
Take square root of the variance - square root of (xi - x)2 / n
What is the SD?
Approximately the average distance of the scores in a data set from the mean - most useful measure of variability
Inflection point
Point where the curve starts bending outward more, always 1 standard deviation from the mean
The z-score formula
z = xi - x(bar) / s
what does the z-score tell us?
How far away a score is from the mean, taking into account the variability of the scores in the data set
The z-score allows us to interpret score in terms of…?
- Relative standing (x) from the mean
- Variability (s) in the distribution by comparing with the standard normal curve
Relative frequency or proportion of cases between two values…
Area under the normal distribution curve bounded by two values
What can be determined by comparing z with standard normal
Can determine what proportion of scores are less than or greater than the individual score
How to give a clear picture of where scores sit…
- Calculate z-score
- Draw a picture
- Look up value of z in z-table to find the relative position of xi
What is a z-table?
It tells us what proportion of values above and below that specific z-value is
properties of the z-distribution
- it isn normal
- x = 0
- s = 1
z-scores are used (as descriptive) to…
- Find the relative position of a data element in its distribution
- Allow comparisons between scores from different distributions
Comparing scores from different distributions
Different distributions may vary in both their mean and SD which makes comparing across different distributions difficult
