Compare two sets of data using averages
We can compare two sets of data using the mean, median and mode.
Take for example the two sets of data shown in the tables below. Since the data is grouped one would have to find the midpoints etc to find the mean, median and modal group of both sets of data (see http://cribbd.com/learn/maths/datahandling/findaveragesfromgroupeddata for more information)
Height(cm)  Number of students 
140149  7 
150159  9 
160169  5 
170179  3 
180189  1 
The mean for this set of data is 157.3, the median is 150159 and the mode is also 150159
Height(cm)  Number of students 
140149  3 
150159  7 
160169  9 
170179  5 
180189  1 
The mean for this set of data is 161.8, the median is 160169 and the mode is also 160169.
If you imagine the two sets of data above graphed, you can see that the bar graph would peak at different places. The first set of data shows that more people are less than 160cm in height, whereas the second set of data shows that most people are between 150cm and 180cm in height.
If the mean of both data sets were the same, one could look at the different averages as well as the range of the data to investigate whether or not the actual data was similar.
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