# MandysNotes

## Mandy's Notes

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### Mean vs. Median - Which is Better?

22 January 2010

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!

### Mu = Mean

22 January 2010

The Greek lowercase letter for "M" (pictured above on the right) is pronounced as "mew."

This symbol represents the mean of a data set.

### 68-95-99.7 (Empirical) Rule

22 January 2010

The EMPIRICAL RULE, otherwise known as the 68.26-95.44-99.74 RULE, says the following:

1) 68.26% of all observed data values will fall between ONE standard deviation to the RIGHT or LEFT of the mean.

2) 95.44% of all observed data values will fall between TWO standard deviations to the RIGHT or LEFT of the mean.

3) 99.74% of all observed data values will fall between THREE standard deviations to the RIGHT or LEFT of the mean.

This is what the illustrated version of the Empirical Rule looks like:

EXAMPLE:

If we are told that the mean of our data is 100, and the standard deviation is 10, then we know the following:

1) 68.26% of our data will fall between 90 and 110.

2) 95.44% of our data will fall between 80 and 120.

3) 99.74% of our data will fall between 70 and 130.

Disclaimer: I did not create nor do I own these videos.  I have simply embedded them, courtesy of YouTube.

### What is a Sample?

22 January 2010

A SAMPLE is a sub-set of the POPULATION.

A SAMPLE is drawn to represent the population, negating the need to conduct an extensive census.

An example of a sample would be:

You decide you want to take a survey of the student body at your school.  Without a team of helpers, it will be nearly impossible to survey EVERYONE in a short period of time.  So instead, you decide to draw a SIMPLE RANDOM SAMPLE, which you determine is representative of the population.

Studying and drawing CONCLUSIONS from a sample would be a heck of a lot easier than trying to survey every person (and study every person) in the Population

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