in this video we're going to focus on calculating the mean median mode and range so let's begin let's say if we have the numbers 12 7 14 5 7 11 and 9 so how can we calculate the mean of this data set what would you do to find it to find the mean which is basically the average of the seven numbers you need to take the sum of the seven numbers and divide it by the numbers that you have which is seven and so that's how you can calculate the average or the arithmetic mean so let's go ahead and do that so let's add up 12 + 7 + 14 + 5 + 7 + 11 and + 9 and since there are seven numbers let's divide it by seven so the sum of the seven numbers is 65 65 / 7 is equal to 9. 285 or 286 if you round it so that's the arithmetic mean of those numbers now what about the median how can we calculate the median of this data set what do you think we need to do in order to find it to find a median it's going to help if you arrange numbers in increasing order the lowest number is five and then we have 27s next we have a 9 11 12 and 14 now in order to find the median we need to find the middle number the best way to find a middle number is to eliminate the first and the last number next eliminate the second number and the second to last number and then eliminate the third and the second or the third one from the left the one in the middle is the median so in this example the median is equal to 9 now what about the mode how can we calculate the mode the mode is simply the number that appears most most often or the number with the highest frequency every number appears once except seven seven appears twice so the mode is equal to S now the last thing that we need to calculate is the range so how can we find the range of this data set the range is simply the difference between the highest number and the low lowest number the highest number is 14 the lowest number is 5 14 - 5 is 9 and so 9 is equal to the range now let's work on another example so let's say if we have a data set that contains the numbers six 14 8 5 3 11 and 9 so go ahead pause the video and try this practice problem find a mean median mode and range when you finish just unpause it and see if you have the right answer so let's start with the mean so let's find a sum let's add up the seven numbers 6 + 14 + 8 + 5 + 3 + 11 + 9 adds up to 56 and there are seven numbers so we're going to divide it by 7 56 / 7 is 8 so the average or the arithmetic mean is equal to 8 so now let's go ahead and calculate the median but to to do that let's arrange it in increasing order the lowest number is three the next one is five and then we have 6 8 9 11 and 14 notice that the middle number is eight so therefore the median is equal to 8 now what about the mode what is the value of the mode in this problem which number occurs most frequently notice that every number occurs only once so therefore there's none there is no mode in this particular problem now the last thing that we need to figure out is the range which is the difference between the highest number and the lowest number the highest number is 14 the lowest number is three and so 14 - 3 is equal to 11 and so that's the range so far we've considered two examples in which we had an odd number of numbers in a data set in this case there was only seven numbers but what if we have an even number of numbers for example let's say if there are eight numbers in a data set let's try this example let's say the numbers are six 8 5 5 9 8 10 and 8 so go ahead take a minute calculate the mean median mode and range so let's start with the mean let's add up the numbers 6 + 8 + 5 + 5 + 9 + 8 + 10+ + 8 will give us a sum of 59 and there are eight numbers now 59 / 8 is equal to 7375 and so this is the average now let's calculate the mode now before we do that let's put the numbers in increas in order as we did before so the lowest number is five there's two of them and then we have a six there's three eights there's a nine and there is a 10 so notice that eight is the number that occurs most frequently there's three of them so the mode is eight now the median is going to be the middle number let's see we can get rid of 5 and 10 5 and 9 6 and six in this case the last two in the middle are eight because they're the same the median is going to be eight now the last thing that we need to calculate is the range and we know the range is simply the difference between the highest number and the lowest number so it's 10 minus 5 which is equal to 5 now let's work on one more example this time we're going to have 10 numbers in a data set instead of eight so the numbers are 12 15 21 4 36 15 11 48 29 and 38 so let's begin by by calculating the mean let's add up the 10 numbers so the sum of the 10 numbers is 229 229 / 10 will give us an average of 22.9 so that's the arithmetic mean now let's calculate the median so let's put everything in order the lowest number is four and then we have 11 and then 12 there's 2 15s next we have 21 29 36 and then 38 and 48 now let's calculate the mode 15 is the number that appears most frequently so the mode is going to be 15 now to find the median we need to calculate the middle number what do you think the middle number is going to be well we can eliminate 4 and 48 next we can get rid of 11 and 38 and then 12 and 36 and then 15 and 29 so at this point we're left with two numbers in the middle whenever you encounter in a situation like this what you need to do is take the average of the two numbers add up the two numbers and divide by two this will give you the midpoint between 15 and 21 the middle number is 18 15 + 21 is 36 half of 36 is 18 so that's the median that's the midpoint between 15 and 21 now lastly let's calculate the range the highest number is 48 the lowest number is 40 and that gives us a difference of 44 and so that's it for this video