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Why is the mean the standard partner of the standard deviation?
The mean and standard deviation often go together because they both describe different but complementary things about a distribution of data. The mean can tell you where the center of the distribution is and the standard deviation can tell you how much the data is spread around the mean.
What does the standard deviation tell us?
standard deviation is the square roots of variance, a measure of spread or variability of data . it is given by (variance)^1/2
What is the difference from having a standard deviation that is a sample and population and how do you tell which one is suited for the question.?
A standard deviation for a sample makes a judgment on the whole data set whereas the population standard deviation uses the shole data set. If the questions says for example, a sample of 50 peoples height was taken... you would use the sample method but if you were asked : "Everyone in the class had their height measured" you could use the population method Hope that helps
What does the standard deviation of a set of data tell you?
It tells you how much variability there is in the data. A small standard deviation (SD) shows that the data are all very close to the mean whereas a large SD indicates a lot of variability around the mean. Of course, the variability, as measured by the SD, can be reduced simply by using a larger measurement scale!
What does the standard deviation of a data set tell us about the data and why is the standard deviation an important measure?
Standard Deviation Explained:Standard deviation is a simple measure of width of a distribution of numbers (usually scores or measurements). It is the next high degree of sophistication of characterizing a bunch of number other than just giving the average ( or mean, median, mode). If you know the average, you do not know how tightly the numbers are clustered around the average, that is what the standard deviation tells you. It is one definition, the most common definition, of the width of a distribution. (There are, of course, many other additional characterizations.)It is important because it tells you if the average is a very useful quantity to use to interpret the data. If someone tells you that the average person your age dies in 50 years, that seems important, but if someone says that the average person dies in 50 years, give or take 20 years, suddenly you realize there is more to the story and maybe you should save more money, just in case. Well, the "give or take" part of that statement is very useful, but not well defined. If they say the life expectancy is 50 years with a standard deviation of 20 years, then that is perfectly defined mathematically. Standard deviation is a mathematical measure of the broadness of the distribution of data.The following two data sets, A and B, have the same mean (average):A: 48, 49, 50, 51, 52B: 30, 40, 50, 60, 70The distribution of the data about the mean in A is very narrow, whereas the distribution about the mean in B is broad. The S.D. gives us a quantification of the broadness of the distribution.In normal distributions, about 68 percent of the data will fall within one S.D. on either side of the mean. About 96 percent of the data will fall with two S.D.Let's say your teacher gives a test to one hundred kids and the test average is 80 points and the S.D. is 10. If the distribution is "normal," about 34 kids will score between 70 and 80, and about 34 kids will score between 80 and 90. We can also predict that about 14 kids will score between 90 and 100, and 14 will score below 70. That leaves four kids. They fall into two groups: they either totally bombed the test, or they got the extra credit question to boost their score over 100!
