Help with statistics??

Question

I'm wanting to know the advantages and disadvantages of using the: mean, median and mode.
This is not related to a specific study but I need to know the general pros and cons of each.
Any help much appreciated.

Answer 1

The mean is generally your best estimator because it is the true average.

However in something like the housing market people often use the median (the middle value). This is because the mean can be weighted more by excessively high values more than low numbers can really bring it down.

The mode (the most reoccurring number) is generally not a very good estimator because there is nothing saying it is necessarily related to the true middle and it could easily just be a number of chance.

Answer 2

Take these numbers 1, 1, 2, 3, 4, 5, 5, 5, 6 and imagine that they are the answer to a question like how many pieces of fruit a person has eaten today.

The mean is the sum of them all divided by how many there are, ie (1+1+2+3+4+5+5+5+6 ) / 9 = 3.55555 pieces of fruit per person.
This is good is you want to find the middle point. However, it can be misleading in that if there some people who eat less and others who eat more. But it gives a middle point..

Using the same numbers, if we look at the data for a modal *(the most frequently occuring number) we would find that result as 5. So the modal would say that people eat 5 pieces of fruit a day.

If we look at the median (the number in the middle of the data set) it tells us people eat 4 pieces of fruit per day. This basically ignores the upper and lower values but in a similar way to the mean, it is a mid point.
This can be altered though because if the data only had 8 peoples answers eg 1,1,2,3,4,5,5,6 the middle number would be between 3 and 4 and so you have to take the mid point of 3 and 4 which is 3.5.

If you think that the mean number of children in a house is 2.4, the median number of children in a house is 2 and the modal number of children in a house is 3 (based on the 1991 survey) you can get an idea of the differences between them all

Answer 3

Mean- is the average of numbers e.g. mean of 7, 8 and 9 is 7+8+9=24 24/3 as there are 3 numbers= 8
Median is the middle number of your numbers ONCE THEY HAVE BEEN PUT IN ORDER (remember that, very important) e.g. the median of 7, 8 and 9 is 8.
Mode is the number which occurs most often in your set of numbers. Well, we can't do that with 7, 8 or 9 can we? So say 7,8,8,9,7,4,1,8. 8 occurs 3 times therefpre its the mode.
Now once we know the definitions, we need to say which is best i.e pros and cons. Well, none of them will be dead on accurate, but they are close.
Mean lets you know, if you have lots of numbers, what the average value is, which comes in useful if you are finding say, your average speed for a journey, as you are never going at the same speed for the whole journey. Though you don't want to find the mean if the question asks says for a questionairre, whichs answer was the most popular- that'd be for the mode.
The median helps you know which is the middle value, which comes in handy if, erm............I can't think why it's useful actually, they just ask it on maths exams.

Answer 4

Each of these is a measure of "central tendency" of a probability distribution, as opposed to standard deviation or variance which measure the dispersion (how far apart values can be).

Mode is really only applies when the distibution can take a fixed number of values such as a dice roll or a coin flip. Simply the value at which the most values occur.

Mean or arithmatic average has many statistical good properties when the distribution is "Normal" or bell shaped. However, skewed distributions such as income--where many people earn a moderate income and a few earn many times more--are best measured by the median.

The median is the point where half of the cases are les than and half the cases are more than the value. For "Normal" distributions the mean and the median are the same.

Answer 5

well think about each one in turn, the median is the middle number when all the numbers are lined up in numerical order - so if you had

1,2, 3, 4, 5, 6, 7, 7, 7,7 ,7 the middle number is 6but it is not necessarily the average as more 7's are shown

i had a brainfart with the other two. sorry.

Answer 6

yes, as already said estimations, but in biz sometimes you have nothing better to work on

Answer 7

erm not accurate sometimes, only an estimate...