A central tendency is a single value that summarises a set of data by representing its central point.
The central tendency of a data set is a single value that summarises the data by representing its central point.
There are three measures of central tendency:
- Mean.
- Median.
- Mode.
Each of these measures has its own advantages and disadvantages.
NoteThe meanis the most commonlyused measure of central tendency.
Mean
The mean is the sum of all the data values divided by the number of data values.
The mean of a data set is the sum of all the data values divided by the number of data values.
The mean is the most commonly used measure of central tendency because it uses all the data values.
NoteThe meanis also known as the average.
Calculating the mean
The mean of a data set is calculated by:
- Adding all the data values.
- Dividing the sum by the number of data values.
The meanis sensitiveto outliers. An outlieris a data valuethat is significantlylargeror smallerthan the other data values.
Median
The median is the middle value of a data set when the data values are arranged in ascending or descending order.
The median of a data set is the middle value of the data set when the data values are arranged in ascending or descending order.
The median is a good measure of central tendency when the data set contains outliers because it is not affected by them.
Calculating the median
The median of a data set is calculated by:
- Arranging the data values in ascending or descending order.
- If the number of data values is odd, the median is the middle value.
- If the number of data values is even, the median is the average of the two middle values.
1. Calculate the mean, median, and modeof the following data set: \$3, 7, 2, 9, 5, 3, 8\$. 2. Which measure of central tendencyis the most appropriatefor this data set? Why?
Theory of KnowledgeHow do different measures of central tendencyinfluenceour interpretationof data? Can the choiceof measurebe manipulatedto supporta particular argument?
