Mean Median Mode

Today we learned a lot about Mean, Median and Mode. We also talked a little on Range, IQR, Variance, and Standard Deviation. These homework problems have been the hardest to do, but not because I don't understand but because it is just a lot of work. A lot of times people get scared when they see that there is a lot do where in actually it is pretty easy to do. So to help you in this I will do a problem where I can show you how easy it really is. First we must have a set group of numbers: 90, 60, 70, 80, 40, 30, 60, 10, 50, 20  With these number the very first thing I want to do is rearrange them from least to greatest: 10, 20, 30, 40, 50, 60, 60, 70, 80, 90 (This will make it much easier later on) Lets first start of with Mean, which means average. To do that we add up all the numbers and divide by how many there are, in this case there are 10 set of numbers.

10+20+30+40+50+60+60+70+80+90=510
510/10=51  Mean=51

We will now do the Median. We will do that by seeing which number is in the middle. If there are an even amount of number then you take the middle two and divide by two. If not just take the middle number at that is your answer. Since we have a even amount of numbers (10) we will take 50+60 and take that answer and divide it by two

50+60=110
110/2=55  Median=55

Next we will do the Mode. All you have to do is find which number is repeated most often, if there are a couple number that repeat the same amount of times, them put both of them, but if there isn't any you say there is no mode. In this case 60 is repeated most often and so the Mode=60

Now let us find the Range. To do that you will need get the largest and smallest number, in our example 90 and 10. All you have to do is subtract 10 from 90 and that is your Range.

90-10=80  Range=80

To help us find the IQR here is a website that I found that uses pictures just is case you don't understand my explanation. It gives the examples if there were an even amount of numbers and odd amount of numbers.   How To Find IQR

IQR means Interquartile Range. To do that will will need to find the upper and lower quartile. The median of our example is 55. So to find the lower quartile we need to take all the numbers from our group of numbers that are lower than 55, which are 50, 40, 30, 20, 10. We then take the Median of that set of number which is 30. So our Lower Quartile is 30. We now must get our higher quartile where we use all the numbers higher than 55, which are 60, 60, 70, 80, 90. The Median of this set of numbers is 70. So our Upper Quartile is 70. To find the IQR we need to subtract our lower quartile from our upper quartile.

70-30=40    IQR=40

We now must find the Variance. These next two part the Variance and Standard Deviation are probably the longest so don't get frustrated, here we go. We must first subtract the Mean from each of our numbers, our Mean was 51 so subtract 51 from all the numbers we started with

10-51= -41
20-51=-31
30-51=-21
40-51=-11
50-51=-1
60-51=9
60-51=9
70-51=19
80-51=29
90-51=39

We now must square them so they will all become positive numbers.

-41x-41=1681
-31x-31=961
-21x-21=441
-11x-11=121
-1x-1=1
9x9=81
9x9=81
19x19=361
29x29=841
39x39=1521

We will now add the sums of the squared numbers, and then divide by 10 because that is how many there are

1681+961+441+121+1+81+81+361+841+1521=6090
6090/10=609   Variance=609

Now with Standard Deviation all you have you do is take the square root of your answer  for the Variance which was 609

Square root of 609=24.67792536

Standard Deviation=24.8 (Rounded to the nearest tenth)

As you can see it is pretty lengthy but not difficult at all. I hope that this helped you out.