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What does a high/low standard deviation mean in real terms?
WEBSep 22, 2017 — The higher the standard deviation the more variability or spread you have in your data. Standard deviation measures how much your entire data set differs from the mean. The larger your standard deviation, the more spread or variation in your data. Small standard deviations mean that most of your data is clustered around the mean. In the …
Socratic.orgThe Standard Normal Distribution - Statistics - Socratic
WEBThe machine does not put exactly 1000 g in every bag. The standard deviation may be in the order of 10 g. 50% will be underweight and 50% will be overweight, by varying amounts, of course. (so 16% will weigh more and 16% will weigh less, as the normal distribution is completely symmetrical). So 2,5% will be under 980 gram and 2.5% over 1020 gram.
Socratic.orgWhat does the standard deviation of a data set describe?
WEBOct 22, 2015 — Explanation: The standard deviation of a data set describes the difference between the data in the set and their mean. The simpliest interpretation could be: "The higher deviation, the more differences there are in the data set". It is rarely non-zero. In fact, as far as I know, the only possibility for a data set to have zero deviation is when
Socratic.orgHow does an outlier affect the mean of a data set? - Socratic
WEBMay 17, 2017 — The mean will move towards the outlier. The mean is non-resistant. That means, it's affected by outliers. More specifically, the mean will want to move towards the outlier. Think about it this way: Let's say we have some data. 1,2,3. The mean of this is 2. But if we add an outlier of 94 to the data set, the mean will become 25. As you can see, …
Socratic.orgCan the standard deviation ever be negative? - Socratic
WEBDec 19, 2014 — The answer to this, is no. Conventionally when taking the square root we only take the positive value. The concept that a negative value appears come from a frequently omitted step and/or a not very known fact. x2 = a. √x2 = √a. So far so good, but you see, the definition of the absolute value function is √x2, so we have.
Socratic.orgCan the standard deviation be greater than the mean? - Socratic
WEBJan 12, 2015 — In a perfect normal distribution it can be. In the ideal normal distribution ALL values are theoretically possible, from -oo to +oo. And then any standard deviation sigma is possible In the real world we work with datasets, that can often be well descibed by a normal distribution. Say you have a filling machine for kilo-bags of sugar. The actual …
Socratic.orgAddition Rules for Variances - Statistics - Socratic
WEBYou cannot just add the standard deviations. Instead, you add the variances. Those are built up from the squared differences between every individual value from the mean (the squaring is done to get positive values only, and for other reasons, that I won't delve into). Standard deviation is defined as the square root of the variance.
Socratic.orgIf the mean, actual observed values, and standard deviation are
WEBOct 7, 2017 — Yes, it does. A z-score is a measure of how many standard deviations from the mean an observation is. Its formula is: z=(x-mu)/sigma where z is the z-score, x is the observation, mu is the mean, and sigma is the standard deviation. If we double the observation (to 2x), double the mean (to 2mu), and double the standard deviation (to …
Socratic.orgFor a normal distribution, what is the probability that the - Socratic
WEBNov 22, 2017 — P(-0.5 <= Z <= +0.5) = 0.383 For a normal distribution, if we are using the standard normal distribution N(0,1^2), a z-score of +0.5 represents a half of a standard deviation above the mean mu. A z-score of -0.5 represents a half of a standard deviation below the mean mu. This question is asking about the area under the normal distribution …
Socratic.orgHow does r squared related to standard deviation? - Socratic
WEBJun 7, 2015 — 2 Answers. R-squared measures how well the regression line fits the data. This is why higher R-squared values correlate with lower standard deviation. The easiest way to see this is by playing with a data set in a spreadsheet software: make a dot plot, right click on a point to add a regression line, and tick the option to show the R-squared.
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