Measures of Dispersion (and skewed) Flashcards
Measures of central dispersion are descriptive statistics. What are these two things?
The range and standard deviation.
What is the range and how is it calculated?
This is calculated by taking the smallest score away from the largest score. This helps us indicate how spread out the data is. However, it is affected by extreme scores so not appropriate for data sets with outliers- it doesn’t tell us if scores are bunched up around the mean.
What is standard deviation? What does a high and low one mean?
Standard deviation is found by using a formula- it tells us the average amount each score ‘deviates’ from the mean: what is the average amount each score differs from the mean?
A high SD indicates a data set where scores are spread out away from the mean, a low SD indicates a data set where scores are bunched close together around the mean. The SD can be seen as more useful than the range as all values are taken into account, therefore outliers have less of an effect on the measure of dispersion.
What is an example of how standard deviation works in groups?
In group 1, there are lots of men roughly in the middle, and one tall man and one short man.
In group 2, you’ve got lots loads of men at the taller end and loads of shorter men at the shorter end but fewer in the middle.
The heights are less consistent in Group 2 than Group 1- they devise more from the mean. So it can be said that group 2 has a greater standard deviation than Group 1.
There is a formula used to calculate standard deviation. what are the rules you need to use it?
1) Work out the mean of all the values.
2) Find (x-x_)^2 for each value.
3) Add these numbers together and divide the total by the number of values mins one.
4) Take the square root of your answer.
How can standard deviation help you understand your results?
It is a better measure of spread than the range because it is less affected by extreme values. But it takes longer to calculate.
It helps you make conclusions.
What does distribution do, what does it represent and what do you need to set up your graph?
Tells you how spread out data is ( in the middle, higher or lower end). They represent the average and spread of a set of data.
Once you know the mean, median and mode, you can tell which distribution your data has.
What does a normal distribution require?
When the mean, median and mode are equal and all in the middle.
It is symmetrical- exactly the same on both sides.
What does a positively skewed distribution require?
When the graph follows mode < median < mean.
It is a skew to the RIGHT- it has a long tail on the right.
What does a negatively skewed distribution require?
When the graph follows mean < median < mode.
It is a skew to the LEFT- it has a long tail on the left.
Where is the median always put on a graph?
The middle.
Where is the mode on certain points of graphs?
It is always at the highest point on the graph- the most common value.
