Measures Of Central Tendancy And Dispersion Flashcards
(16 cards)
What is the mean?
The mean is calculated by adding up all the data items and dividing by the number of data items.
Strengths of the mean
+The mean is the most sensitive measure of central tendency because it takes account of the exact distance between all the values of all the data.
+ It is necessary for further statistical analysis e.g. standard deviation
Weaknesses of the mean
-This sensitivity means that it can be easily skewed by anomalies and thus end up being less representative of the data as a whole.
- It cannot be used with nominal data
- Nor does it make sense to use when you have discrete values as in average number of legs.
What is the median?
The median is the middle value in an ordered list. All data items must be arranged in order and the central value is then the median.
(If there are an even number of data items there will be two central values. To calculate the median add the two data items and divide by two.)
Strengths of the median
+The median is not affected by extreme scores so can be useful under such circumstances.
+It is appropriate for ordinal data and can be easier to calculate than the mean.
Weaknesses of the median
-The median is not as ‘sensitive’ as the mean because the exact values are not reflected in the median.
- It is not useful for further statistical analysis
What is the mode?
The mode is the value that is most common data item.
With nominal data it is the category that has the highest frequency count. The modal group is the group with the greatest frequency.
If two categories have the same frequency the data have two modes, i.e. are bi-modal.
With interval and ordinal data it is the data item that occurs most frequently.
To identify this the data items need to be arranged in order.
Strengths of the mode
+The mode is also unaffected by extreme values and is much more useful for discrete data
+ The only method that can be used when the data are in categories, i.e. nominal data.
Weaknesses of the mode
- It is not a useful way of describing data when there are several modes (like in interval/ratio data).
- Not useful if the distribution is skewed as it won’t display centre of data
What is the range?
The range is the arithmetic distance between the top and bottom values in a set of data.
Strengths of the range
+ It gives an indication of the consistency/reliability of the data
+ It is relatively easy to calculate in comparison to standard deviation
Weaknesses of the range
- Is affected by extreme values because values at highest and lowest end of set are used and these may not actually reflect the data set accurately
- Fails to take into account the distribution of the numbers, meaning it does not indicate whether most numbers are closely grouped around the mean or spread evenly
What is standard deviation?
A more sophisticated way of calculating (as uses all scores) how much each score (in a data set) deviates from the mean. The larger the SD, the greater the variation of scores in a data set.
Strengths of standard deviation
+ Is a precise measure of dispersion because all the values are taken into account. This means that we know whether values are closely grouped around the mean or spread out
+ It is not as affected by extreme values because it does not just look at highest and lowest value in a data set (like the range does)
Weaknesses of standard deviation
- It may hide characteristics of the data, like extreme values because it indicates how far each value is rather than looking at
values at each end of the data set - Time consuming to calculate in comparison to the range
Method to calculate SD
1- Work out the mean for the data set
2- Subtract the mean from each data point
3- Square the result
4- Add these up
5- Divide by n-1
6- Finally calculate the square root
