## Mandy's Notes

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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!

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

**This symbol represents the mean of a data set. **

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.

**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. **