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# Topic: Mean deviation

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 Mean - Wikipedia, the free encyclopedia Sample mean is often used as an estimator of the central tendency such as the population mean. The standard deviation is the square root of the average of squared deviations from the mean. The mean is the arithmetic average of a set of values, or distribution; however, for skewed distributions, the mean is not the same as the middle value (median), or most likely (mode). en.wikipedia.org /wiki/Mean   (906 words)

 Absolute deviation -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-09-17) Typically the point from which the deviation is measured is the value of either the (The value below which 50% of the cases fall) median or the (An average of n numbers computed by adding some function of the numbers and dividing by some function of n) mean of the data set. The average absolute deviation of a data set is the (A statistic describing the location of a distribution) average of the absolute deviations and is a (Click link for more info and facts about summary statistic) summary statistic of (Click link for more info and facts about statistical dispersion) statistical dispersion or variability. In general, the average absolute deviation from the mean is between one and two times the average absolute deviation from the median; it is also less than or equal to the (The square root of the variance) standard deviation. www.absoluteastronomy.com /encyclopedia/a/ab/absolute_deviation.htm   (264 words)

 [No title] The variance is the mean of the squared deviations from the mean (sum of squares). The standard deviation is the square root of the variance (the variance is the square of the standard deviation). Deviation formulas are easier to understand (it is easy to see that distance from the mean is the basic unit of analysis) but they are not as good for computational purposes due to rounding errors. www.andrews.edu /~thayerj/EDRM611/Summer2001ObjectivesUnit4.htm   (1852 words)

 Chapter 2   (Site not responding. Last check: 2007-09-17) Deviation scores sum to zero and thus their mean is always zero. The transformation to deviation scores changes obtained scores below the mean into negative numbers, scores above the mean into positive numbers, and anchors the mean of the distribution at the zero point. The mean is the unique point in a distribution from which the sum of squared deviations is least. www.public.asu.edu /~fmarti3/course/edp502/chap2.html   (561 words)

 comparing test scores The mean is the average score of a distribution, and is computed by adding all the scores together and then dividing by the total number of scores. So standard deviation is the typical, or *average, deviation between individual scores in a distribution and the mean for the distribution." (Urdan, 2001). In a normal curve, the curve is symmetrical around the mean, with the number of scores decreasing as we move in either direction from the midpoint. www.coe.usu.edu /psyc/slehman/nrt/score_comp.htm   (2093 words)

 Behavioral Statistics in Action The formula reads: sigma (standard deviation of a population) equals the square root of the sum of all the squared deviation scores of the population (raw scores minus mu or the mean of the population) divided by capital N or the number of scores in the population. The formula reads: capital S (standard deviation of a sample) equals the square root of the sum of all the squared deviation scores of the sample (raw scores minus x bar or the mean of the sample) divided by lower case n or the number of scores in the sample minus 1. The formula reads: capital S (standard deviation of a sample) equals the square root of the sum of all the frequencies multiplied by the square of their deviation scores and then the entire numerator is divided by the sample size minus 1. www.miracosta.cc.ca.us /Home/rmorrissette/Chapter05.htm   (1317 words)

 AVEDEVMEAN(<>) The average deviation (also known as the mean deviation) is the average absolute difference between the observed values and the arithmetic mean (average) for all values in the data set. The term average deviation is something of a misnomer, since by definition of the mean the sum of all deviations about the mean are zero except for possible rounding errors. For estimating population standard deviation in a normal population, the mean deviation is not as efficient as the sample standard deviation. www.oledb.org /products/connx/InfoNaut/connxcdd32f/avedevmean_numeric_value_.htm   (447 words)

 Measures of Variability Deviations of data values to the left of the mean will be negative numbers, deviations of data values to the right of the mean will be positive values, and the positive and negative values exactly cancel out. The mean deviation was a good idea in that it took into account the values of all of the observations, but it failed to be useful because of exact cancellation between positive and negative deviations. Thus a comparatively large value for the standard deviation is an indication of considerable variability in the data, whereas a comparatively smaller value for the standard deviation is an indication of less variability in the data. www.math.bcit.ca /faculty/david_sabo/apples/math2441/section3/variability/variability.htm   (2195 words)

 Standard Error of the Mean   (Site not responding. Last check: 2007-09-17) Standard Deviation: The standard deviation is the square root of the average squared deviation from the mean. The resulting estimate of the standard deviation of sample means is called the standard error of means and can be interpreted in a manner similar to the standard deviation of raw scores. Example: Suppose that the population mean of males' serum uric acid levels is 5.4 mg per 100 ml and the standard deviation is 1. research.med.umkc.edu /tlwbiostats/stnderrmean.html   (755 words)

 PSC/IR 693   (Site not responding. Last check: 2007-09-17) Mean deviation:  the average difference, in absolute value, of a variable from its mean Variance:  the average of the squared deviations from the mean The sample mean has a distribution with a finite variance (the normal distribution)... www.maxwell.syr.edu /maxpages/classes/psc693/notes/week3/html/psc693_week3.htm   (1113 words)

 Basic Statistics Review - Unit 1 - 165 The standard deviation of the population is 1.63299. The standard error of the mean estimates the error in predicting a population mean from a sample mean. Let’s consider a population with a mean of 100 and a standard deviation of 16. www.msu.edu /user/sw/statrev/strv165.htm   (414 words)

 Review of IDS 270 Variation around this mean follows the normal distribution with a standard deviation of 0.5 fluid ounces. A sample of scores of UIC MBA students is to be taken to estimate the mean in that population. In a test of the null hypothesis that the mean is 18 versus alternatives that the mean is greater than 18, a sample of n = 100 observations gave a mean of 19.5 and standard deviation of 6.00. www.uic.edu /classes/idsc/ids571/bs12revu.htm   (1049 words)

 Descriptive Statistics In general there is a relationship between the fraction of the included data and the deviation from the mean in terms of standard deviations. With the usual standard deviation you add or subtract the standard deviation from the mean in order to test for fractions of included data; with the log standard deviation, you multiply or divide. The standard deviation of the counts in the repeated experiments should be close to the square root of 1000 (31.6). www.physics.csbsju.edu /stats/descriptive2.html   (1632 words)

 Lecture Notes 3 Even though the mean is sensitive to extreme values (i.e., extremely large or small data can cause the mean to be pulled toward the extreme data) it is still the most widely used measure of location. For example, the sum of the deviations of the numbers in a set of data from the mean is zero, and the sum of the squared deviations of the numbers in a set of data from the mean is minimum value. The standard deviation is the square root of 11.5 which is equal to 3.4 inches (expressed in same units as the raw data). business.clayton.edu /arjomand/business/l3.html   (1973 words)

 Moments Likewise, the grouped sample variance (the square of the standard deviation) is proportional to the moment of inertia (a measure of the rotational inertia of an object). Karl Pearson was the first to use the term moment as a descriptor for the sample mean and standard deviation based on the analogy between mechanics and statistics. The sample median is less affected by skewness than the sample mean, i.e., the position of the upper or lower values has little affect on the median (which is the middle value of a ranked dataset). www.stat.wvu.edu /SRS/Modules/Moments/moments.html   (929 words)

 Session 5, Part E: Measuring Variation The mean of the squared deviations is 38 / 9 = 4 2/9, or approximately 4.22. The variance is the mean of the squared deviations, so you could also say that it represents the average of the squared deviations. Compare the standard deviation to the MAD of Line Plot B you found in Problem E2 and to the standard deviation of Line Plot A. Remember that in these problems, the mean is 5. www.learner.org /channel/courses/learningmath/data/session5/part_e/variance.html   (799 words)

 Standard deviation - InfoIndex.org Standard Deviation The standard deviation, like the average deviation, is the measure of the scatter or spread of all values in a series of observations. The standard deviation is a statistical measure of the precision in a series of repetitive measurements. Standard Deviation is a statistical measure of volatility. infoindex.org /l/standard-deviation.htm   (750 words)

 Standard Deviation   (Site not responding. Last check: 2007-09-17) The standard deviation is the square root of the average squared deviation from the mean. The deviation method is considered first, since it closely parallels the concept of standard deviation. First, calculate the mean and determine N. Remember, the mean is the sum of scores divided by N where N is the number of scores. www.med.umkc.edu /tlwbiostats/variability.html   (412 words)

 MATH250 - Printable version of tutorial on measures of dispersion   (Site not responding. Last check: 2007-09-17) Whereas the mean deviation is just that - the mean distance of the measurements from the mean, the standard deviation is usually calculated by the first finding the VARIANCE and then extracting the square root of the variance. The standard deviation is 2 and the variance is 4. The standard deviation is 2 and the variance is 1.41. www.math.ohiou.edu /~just/MATH250/dispersp.htm   (798 words)

 1.3.5.2. Confidence Limits for the Mean Confidence limits for the mean (Snedecor and Cochran, 1989) are an interval estimate for the mean. Instead of a single estimate for the mean, a confidence interval generates a lower and upper limit for the mean. This simply means that noisy data, i.e., data with a large standard deviation, are going to generate wider intervals than data with a smaller standard deviation. www.itl.nist.gov /div898/handbook/eda/section3/eda352.htm   (894 words)

 Statistics 101 - Part 2 It is defined as the square root of the variance, which is the mean of the squares of the deviation from the mean. The sum of the squares of the deviation from the mean is equal to Since 68% of the data values or scores fall within one standard deviation of the mean, and that the curve is symmetric, then it follows that 34% of the data values fall on either side of (one standard deviation from) the mean. www.geocities.com /Athens/Acropolis/7186/stat2.html   (1355 words)

 Mean.gsp The Mean segment is calculated as the arithmetic average of the 5 measured segments. The MAD (Mean Absolute Deviation or Mean Deviation) represents the measurements of the average of the absolute deviations of data points from their mean. Manipulate the line segments and take note of the influence that these manipulations have on the mean and subsequently on the MAD or Mean Deviation. www.mste.uiuc.edu /dildine/sketches/Mean.htm   (250 words)

 Westgard Quality Corporation © 1999, Z-Stats 5: Sum of Squares, Variance, and the Standard Error of the Mean The calculation of a mean is linked to the central location or correctness of a laboratory test or method (accuracy, inaccuracy, bias, systematic error, trueness) and the calculation of an SD is often related to the dispersion or distribution of results (precision, imprecision, random error, uncertainty). Calculation of the mean of the means of samples (the standard error of the mean) The mean of the sampling distribution is always the same as the mean of the population from which the samples were drawn. www.westgard.com /lesson35.htm   (2112 words)

 [No title]   (Site not responding. Last check: 2007-09-17) The standard deviation (denoted by stdev) is almost the square root of the mean (average) of those squared deviations. Standard Deviation: The best general measure of typical deviation is a special kind of average that is formed by adding the squares of the deviations, dividing by one less than the number of measurements, and then taking the square root of the quotient. This means that a polling result stated as 49% (6% has a standard deviation of 3% and means that we are 95% confident that the actual value is in that interval. www.austin.cc.tx.us /mparker/1333/fall04/III_sec5.doc   (2242 words)

 [No title] The objective is to compute the mean and the standard deviation from an array. The sub procedure reads in the numbers from the array (A1..A10), calls up the function procedures and returns the mean and standard deviation value. Note that the standard deviation in this example is for a sample, not a population. www.geocities.com /WallStreet/9245/vba1.htm   (88 words)

 Standard Deviation The "Standard Deviation is referred to as the square root of the Variance. However, when calculating the Standard Deviation of small sample, a better estimate of the parent group is obtained by dividing by (n-1) instead of dividing by "n". The "Standard Deviation" for grouped data can be calculated as in the previous example, but it can also be calculated via the grouped data method. www.bjmath.com /bjmath/Stats/sd.htm   (572 words)

 MABS 67 Statistics, a measure of the degree of scattering of a frequency distribution about its arithmetic mean, equal to the square root of the mean of the squared deviations from the distribution mean. Statistics, the arithmetic average of the absolute values of the individual deviations in a distribution from a central value. Statistics, the average arithmetic mean of the deviations, taken without regard to sign, from some fixed value, usually the arithmetic mean of the data. fog.ccsf.cc.ca.us /~gknapp/stddev.htm   (338 words)

 EDSTAT23   (Site not responding. Last check: 2007-09-17) Converted scores, also referred to as standard scores are based on the standard deviation or distance of a raw score from the mean for a normal curve or distribution. It is used to describe a score's deviation from the mean. For example: a standardized test with a mean of 70 and a standard deviation of 10, a score of 60 would be -10 points from the mean (deviation), divided by the standard deviation (10) equals a z score of -1.00. www.hunter.cuny.edu /edu/apiccian/edstat23.html   (543 words)

 Measures of spread   (Site not responding. Last check: 2007-09-17) It is nice to have a number specifying where data lies (e.g., mean, median), but it is also nice to know how representative of the data that number is (i.e., how far from that number the data lies). For the weights of students the variance is 881.77, and the standard deviation is 29.69. We shall employ the mean being greater than the median as the definition of skewed to the right (although there is a more technical defintion of skewness which does not always agree with this definition). www.math.uni.edu /~campbell/mdm/spread.html   (1176 words)

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