ch 3 b

correlation formula

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five number summary

1. smallest value 2. first quartile 3. median 4. third quartile 5. largest value

for data having a bell-shaped distribution

68.26% of the values of a normal random variable are within +/- 1 standard deviation of its mean >95.44% of the values of a normal random variable are within +/- 2 standard deviations of its mean >99.72% of the values of a normal random variable are within +/- 3 standard deviations

box plot

> graphical summary of data that is based on a five number summary > a key to the development of a box plot is the computation of the median and the quartiles Q1 and Q3 >another way to identify outliers >limits are located using the interquartile range

z-score definition

>a measure of the relative location of the observation in a data set > a data value less than the sample mean will have a z-score less than zero >a data value greater than the sample mean will have a z-score greater than zero >a data value equal to the sample mean will have a z-score of zero

correlation coefficient

>can take on values between -1 and +1 > values near -1 indicate a strong negative linear relationship >values near +1 indicate a strong positive linear relationship > the close the correlation is to zero the weaker the relationship

outlier

>is an unusually small or unusually large value in a data set >a data value with a z score less than -3 or greater than +3 might be considered an outlier

correlation

a measure of linear association and not necessarily causation

data dashboards

are not limited to graphical displays > addition of numerical measures, such a the mean and standard deviation of KPIs, to a data dashboard is critical >dashboards are often interactive

Chebyshev's theorem

at least (1 - 1 / z^2) of the items in any data set will be within z standard deviations of the mean, where z is any value greater than 1 >requires z > 1, but z need not be an integer -At least 75% of the data values must be within z= 2 standard deviations of the mean -At least 89% of the data values must be within z= 3 standard deviations of the mean -At least 94% of the data values must be within z = 4 standard deviations of the mean

covariance formula

formula?

covariance

measure of the linear association between two variables >positive values indicate a positive relationship > negative values indicate a negative relationship

skewness

n ------- x sum of (Xi-X/S)^3 (n-1)(n-2)

drilling down

refers to the functionality in interactive dashboards that allows the used to access information and analyses at increasingly detailed level

moderately skewed left

skewness is negative mean will be less than median

highly skewed right

skewness is positive mean will be more than median

moderately skewed right

skewness is positive mean will more than median

skewness symmetric

skewness is zero, mean and median are equal

z-scores

standardized value Zi = Xi- X ---------- s STANDARDIZE function on excel

empirical rule

used to determine the percentage of data values that must be within a specified number of standard deviations of the mean >based on normal distribution