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6.3 C) Mode & Range
6.3 C) Mode & Range
Mode
The mode is the most frequent value/ option in our data set. To find the mode we simply just look to see what the most common value/ option is. We are going to find the mode for the number of points that our basketball player scored. We are going to use the data from the 9 games and this data is given below.
The mode is the most frequent value/ option in our data set. To find the mode we simply just look to see what the most common value/ option is. We are going to find the mode for the number of points that our basketball player scored. We are going to use the data from the 9 games and this data is given below.
We can see that there are two 22’s in the data set.
This means that the mode for this data set is 22 points.
Another Example – Multiple Modes
The data below gives the number of hours that a runner trains for a marathon per week. What is the mode for this data?
The data below gives the number of hours that a runner trains for a marathon per week. What is the mode for this data?
The mode is the most common value/ option. For the above data set, there are two values that appear twice; both 9 and 12 appear twice. This means that there are two modes for this data set, and this is perfectly fine. Therefore, the modes for the number of hours trained is 9 and 12.
There is no limit for the number of modes that we can have.
Mode – Qualitative Data
We are also able to work out modes for qualitative data.
For example, the table below shows the colours of different cars that drove past a street. Find the mode for the data.
We are also able to work out modes for qualitative data.
For example, the table below shows the colours of different cars that drove past a street. Find the mode for the data.
The mode is the value that appears the most. For this example, it is the colour that has the highest frequency. Black in the table above has the highest frequency and this means that black is the mode.
Range
The range shows us how spread out the data is; a larger range means that the data is more spread out and a smaller range means that the data is closer together/ less spread out. The range is the difference between the largest and smallest value in our data set. The formula for working out the range is:
The range shows us how spread out the data is; a larger range means that the data is more spread out and a smaller range means that the data is closer together/ less spread out. The range is the difference between the largest and smallest value in our data set. The formula for working out the range is:
Let’s work out what the range is for our basketball example. The data for the number of points that our basketball player scored is given below (I have chosen to use the ordered data, but you do not need to use the ordered data to find out the range).
The largest value in our data is 39 and the smallest value in our data is 12. Therefore, the calculation for the range is:
The range for our data is 27.