Where is one value in relation to the rest of the data?
When you have a lot of data, normally over 100 pieces of data, sorting it into percentiles may be a good idea. The data will be divided into 100 sections (percent = per 100). We often see this with nationwide Statistics, like a child's height in the 65th percentile.
Percentiles:
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Similar to percentiles, quartiles are good for large amounts of data, but can also be useful when there is under 100 pieces of data. The quartiles are found by finding the median of all the data (Q2), then the medians of the 'halves' of data (Q1 & Q3).
Quartiles:
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The main 'averages' are the mean, median, mode, and midrange. The Mean and Median are terms most people are familiar with.
The Mean is the arithmetic average, where you add all your pieces of data and divide by how many there are.
The Median is the physical middle of the data.
The Mode is the piece of data that occurs most often.
The Midrange is when you take the smallest & largest and only 'average' those 2.
Central Measures By Hand:
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Central Measures In Excel:
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When you want to know how far a piece of data is from the mean, the Standard Deviation is the calculation you need. This calculation with the Empirical Rule will help you keep track of how much of the data is within a certain 'distance' from the mean.
Standard Deviation By Hand:
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Standard Deviation In Excel:
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Excel Data Analysis ToolPak:
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Another tricky but useful calculation, is the Correlation Coefficient, r. When r is close to 1 or -1 there may be a relation bewteen the two variables, when it is close to 0 there is no relation between them. Do not confuse relation with cause and effect.