If the mean of a data set is larger than the median, it means that the data set is skewed to the right. This happens when the data set has one or a few larger values that drive up the mean but do not affect the median.
2, 3, 4, 5, 6, 7, 10, 12, 14
Practice makes perfect
We are asked to create a data set that contains 8 to 12 values such that the mean is greater than the median. Before we do that, let's think of what does it mean for a data set to have a mean greater than the median.
Mean > Median
Mean is the average of a data set. Mathematically, it is the sum of all of the data values divided by the number of values in a data set.
Mean=Sum of values/Number of values
Now, median is the value that lies in the middle of a data set.
Median=Middle value
Here are the rules to finding the median of a data set.
For an odd number of data points, there is only one value in the middle, and that is the median.
For an even number of data points, the median is the average of the two middle numbers.
If the mean of a data set is larger than the median, it means that the data set is skewed to the left. This happens when the data set has one or a few larger values that drive up the mean but do not affect the median. Let's now give an example of such data set.
2, 3, 4, 5, 6, 7, 10, 12, 14
Because there are nine data points in the set, the middle one is the fifth one. The median of the data set is 6.
2, 3, 4, 5, 6_(Median), 7, 10, 12, 14
Now, let's find the mean of the data set.
&2+3+4+5+6+7+10+12+14/9
&= 7
The mean of the data set is 7. Because 7> 6, the mean of the data set is greater than the median. If we substituted the numbers on the right of the mean with smaller numbers, this may no longer be true. This is because the mean would become smaller.
