Download Math 1: Normal/Binomial Distributions

Notes on Mean Absolute Deviation
---------------------------------------------------------------------------------------------------------------------------Measures of spread, or measures of variability, is statistics used to measure the distribution
of the data in a set.
When a measure of spread is high, then this means that the data is "spread out" or not
consistent.
When a measure of spread is low, then this means that the data is not "spread out" or
consistent.
The first measure of variability to be taught was the interquartile range.
------------------------------------------------------------------------------------------------------------------------------Here are the number of points scored over the last five years for NBA players Kobe Bryant and
LeBron James:
Bryant: {2201, 2323, 2430, 2832, 1819} James: {2304, 2250, 2132, 2478, 2176}
Find the means of both data sets. Based on the means, who is the better scorer per year?
In the financial climate of the NBA, teams like consistency from their players so that they will be
able to accurately measure expectations.
Find the interquartile range for both players. Based on these results, which player is a more
consistent scorer?
------------------------------------------------------------------------------------------------------------------------------Mean Absolute Deviation
Another measure of variability is called the mean absolute deviation. The mean absolute
deviation is the average distance that each value is away from the mean.
If a data set has a small mean absolute deviation, then this means that the data values are
relatively close to the mean. A small mean absolute deviation means the data is consistent.
If the mean absolute deviation is large, then the values are spread out and far from the mean.
A large mean absolute deviation means the data is inconsistent.
------------------------------------------------------------------------------------------------------------------------------Determine the mean of the following set of number of students in 9th grade math classes:
25, 31, 31, 31, 29, 27, 28, 30, 25, 23, 24, 25, 24, 30, 24, 29, 28, 25, 27
Sometimes it is important to see how far away the numbers in a data set are from the mean in
order to determine whether the mean is relevant or not.
If the numbers are all spread apart, the mean might not be a good measure of predicting
outcomes.
For example, if someone in the class gets a 0 on a test, but everyone else in the class gets a B
or an A, the 0 test grade will affect the mean.
The average of the test grades would probably be somewhere close to 70. However, it would
not make sense for me to predict that that a student will get a 70 on the test when everyone
scored an 80 or above except for one student. That is why we find the mean absolute
deviation. The mean absolute deviation is the average amount that each number is away from
the mean of the data set. To find the mean absolute deviation, use the following formula:
Follow these steps:
1)
2)
3)
4)
Find the mean of the data set.
Find the absolute value of the mean minus each entry.
Find the sum of the absolute values
Divide by the number of entries in the data set.
------------------------------------------------------------------------------------------------------------------------------Example: The following are scores on a Math test:
80, 82, 81, 0, 85, 90, 87, 92
Find the mean absolute deviation.
80  82  81  0  85  90  87  92
8
1) The mean of the data set is
= 74.6
2) Now take the mean and subtract if from each number in the data set:
74.6 – 80 = -5.4
74.6 – 0 = 74.6
74.6 – 87 = -12.4
74.6 – 82 = -7.4
74.6 – 85 = -10.4
74.6 – 92 = -17.4
74.6 – 81 = -6.4
74.6 – 90 = -15.4
3) Now add all of the absolute values of the above numbers:
5.4  7.4  6.4  74.6 10.4 15.4 12.4 17.4 = 149.4
4) Now get the mean of the above numbers:
149.4
8 = 18.675
This is the mean absolute deviation.