So I get the general idea: averages include all data points, but means are weighted in some way to reduce the effect of extreme data points.
The formula for averages is easy: add up all the data points, divide by the number of data points, and you’ve got the average.
Is there a standard formula to calculate the mean?
Forgive my squirrely ignorance, but aren’t ‘mean’ and ‘average’ equal in meaning? I believe in statistics they are interchangeable.
Perhaps you are referring to ‘mean’ vs. ‘median.’ Medians are less affected by extreme scores when working with small samples.
Edit:
A median is determined by listing all scores in the sample in either ascending or descending order (doesn’t matter which) and then selecting the score in the middle. Usually they are a better indicator than the mean when the sample size is small.
I’m with seodoa. As far as I know, mean and average mean the same thing. You can calculate where the outliers in your data set are and then exclude them from the mean calculation though, I think.
I’m with everyone else. When a layman uses the term “average”, he typically means “mean.” The two most common of the other methods we use are “median” and “mode.”
I’ve also seen all three methods used in conjunction with additional filters to control the effect of extremes.
In everyday use, mean and average generally have the same meaning. However, in statistics, average means a measure of central tendency. And in that sense there are lots of other averages, such as the median and the mode. There are even more than one mean – the arithmetic mean (add up all the numbers and divide by the number of numbers) and the geometric mean. Many times when you read about some average in the paper it’s the median and not the arithmetic mean.
The Mean is generally understood to be the average…total values/# of values.
The median is the middle value…half-way between the highest and lowest value.
The Mode is the value which repeats most often.
Thank you. I was going to write an elaborate example illustrating the differences between means, medians, and modes and, in particular, why medians are generally preferred in news reports, but I then realized that I was wasting enough time at work as it is.
By the way, if this is work-related, as opposed to just a general question, you’ll want to get the “business side” to clarify how they want for you to handle “ties” in the case of median and mode. While it’s typically not that big of a deal with median, it can sometimes be huge when it comes to the results that mode will return.
No, that’d be determined exclusively by the most extreme values, which is almost never what you want. The median is the value that has half of the values above it and half below it. So, for instance, if your data points are [0,1,2,3,1000000], the median is 2 (it has two values below it and two values above it), but your method would give 500000. Note that the median would be completely unchanged if I replaced that high value with 4, or 3.00001, or a googol.
I think he meant that its rank is halfway between and just phrased it poorly.
One can never be too sure. Too much is at stake on the internets.
Now somebody tell the OP about kurtosis. Me, I’m off to bed.
see - this is why I love the Dope - I post a question with an incorrect assumption close to midnight, and within a couple of hours I have my error corrected and lots of helpful info.
I think I was thinking of the median, not the mean. Thanks for the assistance.
Mode is what I wish more news shows would use.
Why? Mode is not a good measure of central tendency.
To give a real-world example: If you look at all of the registered members here on the SDMB (that is, anyone with a screen name here), the mean number of posts per user is a bit over 128, but the median number of posts is 1, and the mode is 0. About a third of all accounts have never posted at all, and about a quarter have only posted once, but the average is skewed by the relative handful of people who have thousands or tens of thousands of posts.
I’d like to know what number occurs the most not the average, thus the mean.
Example:
American households have 1.5 children. No they don’t. Pleas tell me the greatest number of people have 0 children, 1 child, or 2 children.
OK, for number of children, where there isn’t very much variability, that might be OK. But the problem with the mode is that it just tells you what’s the most common, not how common it is, or how common anything else is. If 51% of households have 2 children, and 49% have 3, then 2 is the mode, but you’d have no clue from that that 3-children households are nearly as common.
And if you’re looking at something like income, which can take many, many different possible values, then the mode becomes almost meaningless: Suppose that there’s a law firm, with the owner making $100 an hour, a couple of senior partners making $92 and $90 an hour respectively (one has a little more seniority than the other), a junior partner making $80 an hour, a paralegal making $40 an hour, an intern making $10 an hour, and a janitor and a custodian both making minimum wage of $6.55 an hour. What’s the typical hourly pay at this law firm? If I tell you that the mode is $6.55 an hour, you’d get a grossly distorted view of the firm.
Having a life is overrated.
Hell, I post here (in the “tens of thousands” range) AND play World of Warcraft! I have negative life!