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Chapter 2: Describing Data- Numerical
Terms in this set (21)
(Or simply the mean), of a set of data is the sum of the data values divided by the number of observations.
the middle observation of a set of observations that are arranged in increasing (or decreasing) order. If the sample size, n, is an odd number, the median is the middle observation. If the sample size, n, is an even number, the median is the average of the two middle observations.
the most frequently occurring value (if one exists). A distribution with one mode is called unimodal, with two modes, bimodal, and with more than two modes, multimodal
x\/g is the nth root of the product of n numbers
Geometric Mean Rate of Return
Gives the mean percentage return of an investment over time
a value such that approximately P% of the observations are at or below that number. !@#!@# separate large ordered data sets in 100ths. (50th percentile is the median).
Descriptive measures that separate large data sets into four quarters.
the five descriptive measures: minimum, first quartile, median, third quartile, and maximum; i. Minimum < Q\/1 < median < Q\/3 < Maximum
The difference between the largest and smallest observations
Measures the spread in the middle 50% of the data; it is the difference between the observation at Q\/3, the first quartile (or 25th percentile);
A graph that describes the shape of a distribution in terms of the five-number summary: the minimum value, first quartile (25th percentile), the median, the third quartile (75th percentile), and the maximum value.
The population !@!@#!!@#, o^2, is the sum of the squared differences between each observation and the population mean divided by the population size, N
s^2: The sum of the squared differences between each observation and the sample mean divided by the sample size, n, minus 1
the population standard deviation, o, is the (positive) square root of the population variance
Alternatively Sample Variance
Coefficient of Variation, CV
a measure of relative dispersion that expresses the standard deviation as a percentage of the mean (provided the mean is positive)
For any population with mean u, standard deviation o, and k >1, the percent of observations that lie within the interval (u+ or - ko) is at least 100[1 - (1/k^2)]%
Provides an estimate of the approximate percentage of observations that are contained within one, two, or three standard deviations of the mean: i. Approximately 68% of the observations are in the interval u + or - 1o.
ii. Approximately 95% of the observations are in the interval u + or - 2o.
iii. Almost all of the observations are in the interval u + or - 3o.
a standardized value that indicates the number of standard deviations a value is from the mean
a measure of the linear relationship between two variables
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