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Standard Deviation and Variance

Standard Deviation and Variance
Deviation just means how far from the normal Standard Deviation The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the greek letter sigma) The formula is easy: it is the square root of the Variance. So now you ask, "What is the Variance?" Variance The Variance is defined as: The average of the squared differences from the Mean. To calculate the variance follow these steps: Work out the Mean (the simple average of the numbers)Then for each number: subtract the Mean and square the result (the squared difference).Then work out the average of those squared differences. Example You and your friends have just measured the heights of your dogs (in millimeters): The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm. Find out the Mean, the Variance, and the Standard Deviation. Your first step is to find the Mean: Answer: Mean = 600 + 470 + 170 + 430 + 3005 = 19705 = 394 so the mean (average) height is 394 mm. So the Variance is 21,704 Formulas Oh No!

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Mean For a broader coverage related to this topic, see average. In mathematics, mean has several different definitions depending on the context. In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution.[1] In the case of a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability P(x), and then adding all these products together, giving .[2] An analogous formula applies to the case of a continuous probability distribution. Not every probability distribution has a defined mean; see the Cauchy distribution for an example.

Mean, Median and Mode from Grouped Frequencies Explained with Three Examples The Race and the Naughty Puppy This starts with some raw data (not a grouped frequency yet) ... Alex timed 21 people in the sprint race, to the nearest second: Normal Distribution Data can be "distributed" (spread out) in different ways. But there are many cases where the data tends to be around a central value with no bias left or right, and it gets close to a "Normal Distribution" like this: A Normal Distribution 7.1.6. What are outliers in the data? The data set of N = 90 ordered observations as shown below is examined for outliers: The computations are as follows: Median = (n+1)/2 largest data point = the average of the 45th and 46th ordered points = (559 + 560)/2 = 559.5 Lower quartile = .25(N+1)th ordered point = 22.75th ordered point = 411 + .75(436-411) = 429.75 Upper quartile = .75(N+1)th ordered point = 68.25th ordered point = 739 +.25(752-739) = 742.25 Interquartile range = 742.25 - 429.75 = 312.5 Lower inner fence = 429.75 - 1.5 (312.5) = -39.0 Upper inner fence = 742.25 + 1.5 (312.5) = 1211.0 Lower outer fence = 429.75 - 3.0 (312.5) = -507.75 Upper outer fence = 742.25 + 3.0 (312.5) = 1679.75 From an examination of the fence points and the data, one point (1441) exceeds the upper inner fence and stands out as a mild outlier; there are no extreme outliers.

Chi-Square Test of Independence This lesson explains how to conduct a chi-square test for independence. The test is applied when you have two categorical variables from a single population. It is used to determine whether there is a significant association between the two variables. For example, in an election survey, voters might be classified by gender (male or female) and voting preference (Democrat, Republican, or Independent). We could use a chi-square test for independence to determine whether gender is related to voting preference. Algebra Problems You may solve a set of 10 questions with their detailed solutions and also a set of 50 questions, with their answers, in the applet to self test you background on how to Algebra problems with detailed solutions Problem 1: Solve the equation 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13

Data Archive The Finnish Social Science Data Archive archives and disseminates quantitative and qualitative research data in digital format. The FSD does not archive research reports or other publications related to archived datasets, nor can these be ordered via the archive. » Read more Data Catalogue FSD's online data service Aila facilitates access to data. Earth Facts - Planet Earth - Earth For Kids The Earth is unlike every other planet in the Solar System in a number of different ways.It is the only planet that has an atmosphere containing 21 percent oxygen. It is the only planet that has liquid water on its surface. It is the only planet in the solar system that has life. The Earth is the only inner planet (Mercury, Venus, Earth and Mars) to have one large satellite, the Moon.