Analyzing Data
Measures of
CENTRAL
tendency
3 Types of Average
Average-representative of the
data
“Typical”
Mean Absolute Deviation:
Deviation refers to the change from the normal or typical behavior.
For data, if we take the average of a set of points, we want to find how
far or different each point is from the average for the set.
Once we find the change of each point, we take the average AGAIN, to
find the average change of each point from the average of the set.
Mean
Mode
1. Add all numbers
together
2. Divide by the amount
of numbers
We are taking the average of the average!
The number that repeats
most often
Range:
Median—the middle number
1.
List data in numerical order (LEAST to GREATEST OR
GREATEST to LEAST)
2. Cross off from top to bottom until you come to the
middle.
3. EXCEPTION TO THE RULE: If you have an even
number of numbers, you will be left with two
numbers. Take the average of these two numbers—
this will give you the median.
How does the data vary? What is
the interval, from what to what?
BIG Number – Little Number
Concert tickets range in price
from $40 to $380.
What is central tendency?
Middle value or value that is representative of data
For example, I am looking to going to a concert with friends. My friends and I want to choose from the following:
Artist
The BEIBS
Rihanna
Chris Brown
Robin Thicke
Pharell
Price Per Ticket
$70
$110
$97
$112
$107
My friends come to me and say, “I know we haven’t decided what concert we are going to, BUT, about how much
should I save up for a ticket?”
In essence, they are asking me to pick a price that would represent the average or typical price for a concert
ticket.
Well, there are three ways I can calculate the average.
Mode: There is no price that repeats, so I can’t use this measure 
Median: 70 97 107 110 112
The median would be $107.
Mean: 70 + 110 + 97 + 112 + 107 = 496
496 divided by 5 = $99.20
Well these three methods were all created to calculate the middle or typical value, sometimes we choose one
measurement for the other, when appropriate. In other words, I want to choose the measurement that BEST
represents my data.
In this situation, I would say, the mean of $99.20 best represents my data, as I feel it is the number that is closest
to the middle. Yes, there are some tickets that are cheaper, and some tickets that are more costly, but it gives
me the best representation of the middle.
Let’s look at the other two and see why they are not the best fit.
The median came out to be $107. I would say that is one of the higher values and not representative of the rest
of my data. It is 37 away from my cheapest ticket, but only 5 away from my highest ticket! This definitely
represents the higher end more!
Mode, well, there was no mode this time. So, it is not applicable in this situation.
Let’s talk about the mean absolute deviation:
The Range:
Overall conclusions:
Miss Piazza loves to go to the Yankee games and pig out on all the amazing food they have there! I get the gluten
free hot dogs, hot chocolate, fries, and ice cream in the Yankee hat. Unfortunately, the Yankees are done for the
season, but it’s not too early to start setting aside money for next year’s games. I want to find the average
amount I spent on food this year at the games, so I can put that money aside for next year. When I went through
my purse and uncrumpled all the receipts, here is what I found.
$15 $27 $17 $40 $35 $29 $35 $32 $38
Let’s use all three measures and see which one best represents the amount I spent on food per game:
Mode:
Median:
Mean:
Which is the BEST measurement and why?
Let’s find out the mean absolute deviation (in other words): how much on average did my spending habits from
each game differ from the average of the overall amount I spent each game?
What was the range?
What overall conclusions can I make?
Average Calories in Fast Food
Place
Burger King
McDonalds
Wendy’s
KFC
Meal
Double Whopper Combo
Big Mac Combo
½ Pounder Combo
3 Drumsticks, mashed potatoes and
soda
**TRUE FACTS: taken from each company’s website!
Let’s see what the best representation is:
Mean:
Median:
Mode:
Calories
1160
920
1290
680
What is the best representation? WHY?
Mean absolute deviation:
The range:
Overall conclusion: