give an example where the median would be less than the mean.
2, 3, 6, 10, 20
Any positively skewed distribution.
Sure! Let's say we have a dataset of the following numbers: 1, 2, 3, 4, 50. To find the median, we first need to arrange the numbers in ascending order: 1, 2, 3, 4, 50. The median is the middle value of a dataset, so in this case, the median is 3, as it is the middle number.
To find the mean, we need to add up all the numbers in the dataset and then divide by the total count. In this case, the sum of the numbers is 1 + 2 + 3 + 4 + 50 = 60. Since there are 5 numbers in the dataset, the mean is 60 / 5 = 12.
From this example, we can see that the median (3) is less than the mean (12). This happens when there is a large outlier, in this case, the number 50. The outlier greatly affects the mean because it is much larger than the other numbers. However, the median is not as affected by outliers because it only considers the middle value, not the actual values themselves.