What is descriptive statistics in mathematics
If, for example, you have a dozen ordinary folks and one millionaire, the distribution of their wealth would be lopsided towards the ordinary people, and the millionaire would be an outlier, or highly deviant member of the group. So once again, you have a bunch of numbers. A slightly more sophisticated measure is the interquartile range.
In SPSSwe have to perform the following steps:. This table summarizes all of the raw data in the form of a table; these descriptive statistics are also used for comparison. Your committee and the other professional readers of your dissertation will want to know the make-up of your sample and the responses to the questions in your instrument. Descriptive statistics are important for establishing the validity of your sample as a representation of the sampled population.
Including these in your dissertation will allow comparison to other similar studies, while placing your results in perspective. Basic descriptive statistics for education and the behavioral sciences 4th ed.
Descriptive statistics and probability. Descriptive statistics, part II: Most commonly used descriptive statistics. Journal for Specialists in Pediatric Nursing, 8 3 Applying and interpreting statistics: You're somehow trying to represent these with one number we'll call the average, that's somehow typical, or middle, or the center somehow of these numbers. And as we'll see, there's many types of averages.
The first is the one that you're probably most familiar with. It's the one-- and people talk about hey, the average on this exam or the average height.
And that's the arithmetic mean. Just let me write it in.
Introduction to Descriptive Statistics: Using Mean, Median, and Standard Deviation
I'll write in yellow, arithmetic mean. When arithmetic is a noun, we call it arithmetic. When it's an adjective like this, we call it arithmetic, arithmetic mean. And this is really just the sum of all the numbers divided by-- this is a human-constructed definition that we've found useful-- the sum of all these numbers divided by the number of numbers we have.
So given that, what is the arithmetic mean of this data set? Well, let's just compute it. It's going to be 4 plus 3 plus 1 plus 6 plus 1 plus 7 over the number of data points we have.
So we have six data points. So we're going to divide by 6. And we get 4 plus 3 is 7, plus 1 is 8, plus 6 is 14, plus 1 is 15, plus 7. Let me do that one more time. You have 7, 8, 14, 15, 22, all of that over 6. And we could write this as a mixed number. We could write this as a decimal with 3. So this is also 3. We could write it any one of those ways. But this is kind of a representative number.
This is trying to get at a central tendency. Once again, these are human-constructed. No one ever-- it's not like someone just found some religious document that said, this is the way that the arithmetic mean must be defined. It's not as pure of a computation as, say, finding the circumference of the circle, which there really is-- that was kind of-- we studied the universe. And that just fell out of our study of the universe. It's a human-constructed definition that we found useful.
Now there are other ways to measure the average or find a typical or middle value. The other very typical way is the median. And I will write median. I'm running out of colors. Range, quartilesabsolute deviation and variance are all examples of measures of variability. Dictionary Term Of The Day. A financial institution that holds customers' securities for safekeeping so as to Broker Reviews Find the best broker for your trading or investing needs See Reviews.
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You then measure the distance between those two numbers, which therefore contains half of the data. Notice that the number between quartile 2 and 3 is the median! The interquartile range for example is.
The reason for the odd dividing lines is because there are 15 pieces of data, which, of course, cannot be neatly divided into quartiles!
The standard deviation is the "average" degree to which scores deviate from the mean. More precisely, you measure how far all your measurements are from the mean, square each one, and add them all up.
The result is called the variance.
Take the square root of the variance, and you have the standard deviation. Like the mean, it is the "expected value" of how far the scores deviate from the mean. So, subtract the mean from each score and square them and sum: Then divide by 15 and take the square root and you have the standard deviation for our example: One standard deviation above the mean is at about 3. At its simplest, the central tendency and the measure of dispersion describe a rectangle that is a summary of the set of data. On a more sophisticated level, these measures describe a curve, such as the normal curve, that contains the data most efficiently.