Sarah B.

a list or table containing the VALUES OF A VARIABLE and the CORRESPONDING FREQUENCIES with which each value occurs

frequency distribution

Why use frequency distributions?

- it's a way to summarize data
- it condenses the raw data into a more useful form
- allows for a quick visual interpretation of the data

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type of data with a countable number of possible values

used to see how data is spread over different categories

used to see how data is spread over different categories

discrete data

proportion of total observations in a given category

frequency in category/ total # of observations

frequency in category/ total # of observations

Relative frequencey

running sum of relative frequencies

used to stratify customers/products

use to influence decisions (show what you want to show)

used to stratify customers/products

use to influence decisions (show what you want to show)

cumulative relative frequency

use to show trend lines or compare similar data

scatter diagrams and line charts

the arithmetic average of data values

mean

the most common measure of central tendency

mean

sum of values divided by the number of values

affected by extreme values (outliers)

affected by extreme values (outliers)

mean

in an ordered array, this is the "middle" number

NOT affected by extreme values

NOT affected by extreme values

median

sorted data

data array

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the i^{th} position

i=(1/2)n

i=(1/2)n

Median Index Point

Shape of distribution

mean<median

mean<median

left-skewed

shape of distribution

mean-=median

mean-=median

symmetric

shape of distribution

mean>median

mean>median

right-skewed

a measure of location

the value that occurs MOST OFTEN

not affected by extreme values

the value that occurs MOST OFTEN

not affected by extreme values

Mode

used when values are grouped by frequency or relative importance

weighted mean

total spread of data

range

scatter around the mean

sum of squares/(n-1)

sum of squares/(n-1)

Variance

most common use because same units as original sample

square root of sum of squares/(n-1)

square root of sum of squares/(n-1)

standard deviation

measures of this give information on the spread or variability of the data values

variation

compute difference between each value and the mean, square each difference and calculate sum

sum of squares

simplest measure of variation

difference between the largest and the smallest observations

=X_{max} - X_{min}

difference between the largest and the smallest observations

=X

Range

Disadvantage of the range:

ignores the way in which data are distributed

ratio of standard deviation to mean as expressed as %

used to measure variation relative to the mean

measures scatter in the data relative to the mean

used to measure variation relative to the mean

measures scatter in the data relative to the mean

Coefficient of variance

CV= pop. standard deviation/ pop. mean

Population coefficient of variation

CV=sample standard dev./ sample mean

sample coefficient of variance

z> or= +or- 3.0

outlier

the larger the Z score...

the greater the distance from the mean

z=(value-mean)/std dev

Z score

if the data distribution is bell-shaped, then the interval:

mean +or- 1 std dev contains about 68% of the values in the population or the sample

mean +or- 1 std dev contains about 68% of the values in the population or the sample

empirical rule

according to the empirical rule, if the data distribution is bell-shaped, then the interval of the mean +or- 1 std dev contains about this many of the values in the population or the sample

68%

according to the empirical rule, if the data distribution is
bell-shaped, then the interval of the mean +or- 2 std devs contains
about this many of the values in the population or the sample

95%

according to the empirical rule, if the data distribution is
bell-shaped, then the interval of the mean +or- 3 std devs contains
about this many of the values in the population or the sample

99.7%

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