Summarizing data
Now that we know how to collect and organize data, we can move on to the lesson of summarizing data.
We can summarize data, using the 3 measures of central tendency.
These 3 measures of central tendency are the mode, median and the mean.
Arranging data in ascending or descending order is very important. This will help us to calculate the answers faster and to calculate the exact middle (median) of the data set.
Mode:
The mode is the value that appears the most in the data set. A data set can have one mode, two modes or no modes.
In the example above, we can see that the data set has been arranged from small to big and the number 4 appears the most, which means the mode of this data set is 4.
If a data set has two modes, we can say that it is bimodal.
Below is an example of a data set that has 2 modes, which means that this data set is bimodal. The 2 numbers that appears the most is 1 and 5.
Median:
The median of a data set is the middle value of the ORDERED data set.
Most important is to order the numbers in the data set. We can not get the number in the middle if the numbers aren't in ascending or descending order.
Calculating the median of a data set with an even number of values and an odd number of values.
Example of even and odd number values
When there's an odd number of values in the data set, for instance 7, it means that the middle of 7 is 3,5. I can not count 3,5 numbers, so I round it off to the nearest whole. 3,5 rounded off is 4. This 4 means that I count 4 numbers forward and 4 numbers backwards. The numbers that I end on will be the same and that will be the median of the set of data.
When there's an even number of values in the data set, for instance 8 numbers, it means that the half of 8 is 4. That means that I have to count 4 numbers forward and 4 numbers backwards. Other than the odd numbers in the data set, you will see that now, if we count 4 numbers forward and 4 numbers back, I will land on two different numbers next to each other. This means that I have to take these 2 numbers and add them together and then get the middle of the answer. To get the middle, I have to divide the answer with 2, because I've added 2 numbers together. The answer I get will be the median of the set of data.
Another example of the median of 2 sets of data numbers
Mean
The last measure of central tendency is the mean. The mean is the average of all the numbers in the data set.
We can calculate the mean as follow:
The sum of all the values in a data set ÷ the number of values in the data set
Calculate the mean of the data set with numbers:
15, 13, 18, 16, 14, 17, 12
In the example above, there are 7 numbers in total, to calculate the mean of the data, we add all 7 numbers together and divide it by 7 to get the average number of the set of data.