MandysNotes

Mean, Median & Mode

Mean, Median & Mode (6)

Friday, 22 January 2010 23:54

Mean vs. Median - Which is Better?

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Both the mean and the median are measures of center. 

If you have a symmetrical set of data -- IF THE NUMBERS IN THE SET ARE EVENLY SPACED -- the mean and the median will be EXACTLY THE SAME. 


Here is WHY:

If you have a data set: 25, 50, 75

MEAN = (25 + 50 + 75) = 150 / 3 = 50

MEDIAN = 50 (the number bang in the center)

Both values are the same. 


When dealing with skewed data sets (when the numbers are NOT evenly spaced), it is better to use the median to express the center.  It is RESISTANT to extreme values. 

 

Here is WHY:

If you have a data set: 20, 50, 100

MEAN = (20 + 50 + 100) / 3 = 56.6666666

MEDIAN = 50

 

If we make this set even more extreme: 10, 50, 150

MEAN = (10 + 50 + 150) / 3 = 53.333333

MEDIAN = 50

 

No matter how we change the values in this set, if the middle number is 50, the MEDIAN will be 50.  ALWAYS.  

The mean is SENSITIVE to change by every value, and therefore should only be used where the data is normally distributed. 

I always remembered this by memorizing that we are all "sensitive to mean [people]" - but whatever works for you!

Friday, 22 January 2010 20:11

What is the Mode?

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The MODE of a data set is simply the number that appears the most often. 

For example, in this set:  [1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17] - The mode is 6.  This is a UNIMODAL set, and looks like this:

 

In the set: [1, 1, 2, 4, 4] - There are TWO modes (1 and 4), making this set BIMODAL, which looks like this:

 

For sets where there are more than TWO modes, the set is called MULTIMODAL. 

 

Friday, 22 January 2010 19:44

What is the Median?

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The MEDIAN is always the number **BANG** in the middle of any number set. 


If you have: 

25, 50, 75

The MEDIAN is 50. 

With an ODD number of items, the MEDIAN will always be the number directly in the center. 


 

If you have:

25, 50, 75, 100

In an EVEN number of items, the MEDIAN will always be the AVERAGE of the two central numbers. 

Here, the MEDIAN is (50+75)/2 = 62.5

Friday, 22 January 2010 19:35

What is the Mean?

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 So...while I was cruising the net for more learning resources, I found this on a Wiki which defined the MEAN as:

 

Yeeeeah.  In a technical sense, this is correct, but if I saw it in a book without knowing what the squigglies were, I would most certainly freak out. 

 

THIS is exactly the same thing, and a whole lot easier to conceptualize:

 

If you are given 3 numbers, add them up and divide by 3:

 

 

If you are given 4 numbers, add them up and divide by 4:

 

And so on.  The MEAN is the TOTAL SUM of all values you are given, divided by the NUMBER of values you are given. 

 

So this:

Technically means: 1 times the SUM of all the values you are given, divided by the number of values you are given.  (Somehow it's easier to think about in English.  Check out What's with the Greek? later.)

Friday, 22 January 2010 19:30

Sample Mean vs. Population Mean

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The SAMPLE MEAN is the mean of a sample. 

The POPULATION MEAN is the mean of the population. 

Different symbols make the distinction between these two, although the formulas are exactly the same. 

  

 

The ONLY difference between the two is that the SAMPLE MEAN is referred to as "x bar" whereas the POPULATION MEAN is referred to as "mew."  BOTH are found by calculating the SUM of all values you are given and dividing by "N," the number of total values.  

We can often use x bar, the SAMPLE MEAN, to draw conclusions about the mean of the entire population

 

NOTRad