Mathematics/Statistics/Core Measurements: Difference between revisions
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Below are some of the most basic, and regularly used forms of measurements in statistics. | Below are some of the most basic, and regularly used forms of measurements in statistics.<br> | ||
All of these measurements are used to gather information about a list of items. | |||
{{ Note | Most of these are easier to use when the list of items is sorted by some meaningful ordering. For some, such as [[#Median]], they will only work on sorted lists.}} | |||
== Mean/Average == | == Mean/Average == |
Revision as of 13:09, 11 May 2020
Below are some of the most basic, and regularly used forms of measurements in statistics.
All of these measurements are used to gather information about a list of items.
Mean/Average
The "mean" and "average" are effectively two different words for the same thing.
Effectively, this attempts to get the most "middle" value given a set of items.
Standard (Unweighted) Mean
Unweighted Mean is what most people think of when someone says "mean" or "average.
Effectively, take all values in a list and add them together. Then divide this sum by the total count of original values.
Scientific Notation:
Given a list of n terms, [x_0, x_1, ..., x_{n-1}, x_{n}]:
Direct Notation:
Given a list of n terms, [x_0, x_1, ..., x_{n-1}, x_n]:
Example:
Given a list of [1, 4, 7, 5, 9, 9, 2, 10].
Step 1) Sum: 1 + 4 + 7 + 5 + 9 + 9 + 2 + 10 = 47
Step 2) Divide sum by count: = 5.875
Weighted Mean
Weighted Mean is similar to above, except that each value has a "weight" associated with it.
Scientific Notation:
Given a list of n terms, [x_0, x_1, ..., x_{n-1}, x_{n}], with associated weights [w_0, w_1, ..., w_{n-1}, w_{n}]:
Direct Notation:
Given a list of n terms, [x_0, x_1, ..., x_{n-1}, x_n], with associated weights [w_0, w_1, ..., w_{n-1}, w_{n}]:
Example:
Given a list of [1, 4, 7, 5, 9, 9, 2, 10], the first 4 values are twice as important as the last 4. Step 1) Sum: 2*1 + 2*4 + 2*7 + 2*5 + 1*9 + 1*9 + 1*2 + 1*10 = 64 Step 2) Divide sum by weights: = = 5.333
Median
Similarly to mean, the median attempts to get the most "middle" item given a set of items.
However, instead of doing so by literal value, it does this by count of items.
For odd numbered sets, the median is the exact middle number.
Given a list of [1, 2, 3, 5, 7], the median is 3.
For even numbered sets, the median is the middle two numbers.
Given a list of [1, 2, 3, 4, 5, 7], the medians are 3 and 4.
Mode
The mode is the value that occurs most frequently in a set of items.
Given a list of [1, 2, 2, 3, 3, 4, 4, 4], the mode is 4.