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Unformatted text preview: Originally by "‘piccolojunior"’ on the College Confidential forums; reformatted / reorganized / etc by Dillon Cower. Comments / suggestions / corrections: [email protected] 1 • Mean = ¯ x ( sample mean ) = μ ( population mean ) = sum of all elements ( ∑ x ) divided by number of elements ( n ) in a set = ∑ x n . The mean is used for quantitative data. It is a measure of center. • Median: Also a measure of center; better fits skewed data. To calculate, sort the data points and choose the middle value. • Variance: For each value ( x ) in a set of data, take the difference between it and the mean ( x- μ or x- ¯ x ), square that difference, and repeat for each value. Divide the final result by n (number of elements) if you want the population variance ( σ 2 ), or divide by n- 1 for sample variance ( s 2 ). Thus: Population variance = σ 2 = ∑ ( x- μ ) 2 n . Sample variance = s 2 = ∑ ( x- ¯ x ) 2 n- 1 . • Standard deviation, a measure of spread , is the square root of the variance. Population standard deviation = p σ 2 = σ = q ∑ ( x- μ ) 2 n . Sample standard deviation = p s 2 = s = q ∑ ( x- ¯ x ) 2 n- 1 . – You can convert a population standard deviation to a sample one like so: s = σ p n . • Dotplots, stemplots: Good for small sets of data. • Histograms: Good for larger sets and for categorical data. • Shape of a distribution: – Skewed: If a distribution is skewed-left, it has fewer values to the left, and thus appears to tail off to the left; the opposite for a skewed-right distribution. If skewed right, median < mean . If skewed left, median > mean . – Symmetric: The distribution appears to be symmetrical. – Uniform: Looks like a flat line or perfect rectangle. – Bell-shaped: A type of symmetry representing a normal curve. Note: No data is perfectly normal - instead, say that the distribution is approximately normal . 2 • Z-score = standard score = normal score = z = number of standard deviations past the mean; used for normal distributions . A negative z-score means that it is below the mean, whereas a positive z-score means that it is above the mean. For a population, z = x- μ σ . For a sample (i.e. when a sample size is given), z = x- ¯ x s = x- ¯ x σ p n . 1 • With a normal distribution, when we want to find the percentage of all values less than a certain value ( x ), we calculate x ’s z-score ( z ) and look it up in the Z-table. This is also the area under the normal curve to the left of x . Remember to multiply by 100 to get the actual percent. For example, look up z = 1 in the table; a value of roughly p = 0.8413 should be found. Multiply by 100 = ( 0.8413 )( 100 ) = 84.13%. – If we want the percentage of all values greater than x , then we take the complement of that = 1- p ....
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This note was uploaded on 06/11/2011 for the course ACCT 302 taught by Professor Micheal during the Spring '11 term at MSU Billings.
- Spring '11