Range variance standard deviation coefficient

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Unformatted text preview: 25 440 450 465 480 510 575 430 440 450 470 485 515 575 430 440 450 470 490 525 580 435 445 450 472 490 525 590 435 445 450 475 490 525 600 435 445 460 475 500 535 600 435 445 460 475 500 549 600 435 445 460 480 500 550 600 440 450 465 480 500 570 615 440 450 465 480 510 570 615 Interquartile Range The interquartile range of a data set is the difference between the third quartile and the first quartile. It is the range for the middle 50% of the data. It overcomes the sensitivity to extreme data values. Interquartile Range 3rd Quartile (Q3) = 525, 1st Quartile (Q1) = 445 Interquartile Range = Q3 - Q1 = 525 - 445 = 80 425 440 450 465 480 510 575 430 440 450 470 485 515 575 430 440 450 470 490 525 580 435 445 450 472 490 525 590 435 445 450 475 490 525 600 435 445 460 475 500 535 600 435 445 460 475 500 549 600 435 445 460 480 500 550 600 440 450 465 480 500 570 615 440 450 465 480 510 570 615 Variance The variance is a measure of variability that utilizes all the data . The variance is useful in comparing the variability of two or more variables. Standard Deviation The standard deviation of a data set is the positive square root of the variance. It is measured in the same units as the data, making it more easily interpreted than the variance. The standard deviation is computed as follows: s s 2 for a sample 2 for a population Coefficient of Variation The coefficient of variation indicates how large the standard deviation is in relation to the mean. The coefficient of variation is computed as follows: s 100 % x for a sample 100 % m for a population Variance, Standard Deviation and Coefficient of Variation Variance s2 ( x i x )2 n1 2 , 996.16 Standard Deviation s s2 2996.47 54.74 Coefficient of Variation the standard deviation is about 11% of of the mean s 54.74 100 % 100 % 11.15% x 490.80 Part B: 1. Measures of Distribution Shape, Relative Location, and Detecting Outliers 2. Exploratory Data Analysis 3. Measures of Association Between Two Variables 4. The Weighted Mean and Working with Grouped Data Measures of Distribution Shape, Relative Location, and Detecting Outliers • • • • Distribution Shape z-Scores Empirical Rule Detecting Outliers Distribution Shape: Skewness An important measure of the shape of a distribution is called skewness. The formula for computing skewness for a data set is somewhat complex. n xi x Skewness s (n 1)( n 2) 3 Skewness can be easily computed using statistical software. Distribution Shape: Skewness Symmetric (not skewed) -Skewness is zero. -Mean and median are equal. .35 Relative Frequency .30 .25 .20 .15 .10 .05 0 Skewness = 0 Distribution Shape: Skewness Moderately Skewed Left -Skewness is negative. -Mean will usually be less than the median. .35 Relative Frequency .30 .25 .20 .15 .10 .05 0 Skewness = .31 Distribution Shape: Skewness Moderately Skewed Right -Skewness is positive. -Mean will usually be more than the median. .35 Relative Frequency .30 .25 .20 .15 .10 .05 0 Skewness = .31 Distribution Shape: Skewness Highly Skewed Right -S...
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