Intermath: Investigations: Data Analysis: Statistics
Generate two sets of data with the same means but different medians.
We are looking at creating a 2 sets that have the same average but have different median numbers. The easiest way to do this is to have the same total numbers in each set. Let's say that there will be five numbers in each data set. In order for the means to be the same, the total of the data for both sets must be the same! So lets say that the total for our two sets of data will be 100. That's an easy number to work with. Now, I need to pick a set of five numbers that sum to 100. I'll say 10, 15, 20, 20, 35. Let's look at the median number - remember that is the one that is in the middle when the data is written in numerical order. For my first set of data the median number is the third number, or 20.
Now I can create a second set of data that adds to 100, but being careful that when the five numbers are lined up numerically that the third number is NOT 20. Here they are: 10, 10, 10, 10, 60. Here my median number is 10. Just for fun lets find what the mean of a data set with five numbers that total to 100. Or 100/5= 20. That's cool - the median of my first data set was actually the same as the mean.
Generate two sets of data with the same medians but different means.
This will be even easier that the above challenge. First let's choose the number of numbers in each data set - how about 7. So we need to make sure that the fourth number when the sets are lined up numerically is the same, why don't we make the median of our sets 12. So for the first set I create I can say: 3, 6, 9, 12, 13, 14, 15. Which has a mean of 3+6+9+12+13+14+15/7 or 72/7= 10&2/7.
Now I can make a second set of data that has the fourth number of 12, but a totally different mean. What about: 2, 10, 11, 12, 150, 275, 301. The fourth number is still twelve, but now the mean is different. It is 761/7 or 108&5/7. I would say that they definately don't have the same mean.
Generate two sets of data with the same means but different modes.
The mode is the number that occurs most often. This will be very similar to the one done above. First lets choose a number that will be the sum of both sets of data, since the means have to be the same. How about 52. So now lets choose the number of entries that there will be in each data set. Lets say 6. So I need to come up with six numbers that sum to 52, but we should also choose a mode. Lets have a mode of 2 to keep it simple. Now I need 6 numbers that sum to 52 and one of the number 2 must occur the most often in the data set. What about: 1, 3, 2, 2, 18, 26. Now I need to create a different set that sums to 52 but has another mode. Lets say the mode for this one will be 4. What about: 1, 4, 4, 4, 4, 35.
Generate two sets of data with the same modes but different means.
Again, this will be very much like the ones above. This time we don't need to have any regard for the average, except to be sure that they aren't the same. In this one, let's say that the mode will be 6. Remember, the averages can be anything but the same. For the first data set, I'll have: 1, 6, 6, 6, 6, 7. For my second data set, I'll have 1, 6, 6, 6, 25, 64, 123. The modes are both six and the averages are far from the same.