# Shared Flashcard Set

## Details

Definitions--Chapter 3
Introductory Statistics definitions (descriptive measures)
37
Mathematics
02/18/2013

Term
 descriptive measures
Definition
 numbers that are used to describe data sets
Term
 measure of centeral tendency (measures of center)
Definition
 descriptive measures that indicates where the center, or most typical value, in a data set lieoften called averages
Term
 mean
Definition
 sum of the observations divided by the number of observations
Term
 median
Definition
 arrange the data in increasing order.If the number of observations is odd, then the median is the observation exactly in the middle of the ordered list.If the number of observations is even, then the median is the mean of the two middle observations in the ordered listIn both cases, if we let n denote the number of observations, then the median is at position (n+1)/2 in the ordered list
Term
 mode
Definition
 find the frequency of each value in the data setif no value occurs more than once, then the data set has no modeotherwise, any value that occurs with the greatest frequency is a mode of the data set
Term
 resistant measure
Definition
 not sensitive to the influence of a few extreme observations (e.g. median, but not mean)
Term
 trimmed mean
Definition
 more resistant meancreated by removing a percentage of the smallest and largest observations before computing the mean
Term
 sample mean
Definition
 for a variable x, the mean of the observations for a sample is called a sample mean and is denoted as an x with a line over itmean of the sample data
Term
 measures of variation (measures of spread)
Definition
 descriptive measures that indicate the amount of variation or spread in a data set
Term
 range
Definition
 difference between the maximum (largest) and minimum (smallest) observations
Term
 standard deviation
Definition
 measures variation by indicating how far, on average, the observations are from the mean
Term
 deviations from the mean
Definition
 how far each observation is from the mean
Term
 sum of squared deviations
Definition
 the sum of the squared deviations from the mean gives a measure of the total deviation from the mean for all the observations
Term
 Chebychev's Rule
Definition
 valid for all data sets and implies, in particular, that at least 89% of the observations lie within three standard deviations to either side of the mean
Term
 Empirical Rule
Definition
 If the distribution of the data set is approximately bell shaped, then we can apply this rule, which implies, in particular, that roughly 99.7% of the observations lie within 3 standard deviations to either side of the mean
Term
 percentiles
Definition
 divide a data set into hundredths, or 100 equal parts
Term
 deciles
Definition
 divide a data set into tenths, or 10 equal parts
Term
 quintiles
Definition
 divide a data set into fifths, or 5 equal parts
Term
 quartiles
Definition
 divide a data set into quarters, or 4 equal parts
Term
 first quartile
Definition
 the number that divides the bottom 25% from the top 75%
Term
 second quartile
Definition
 the number that divides the bottom 50% from the top 50%median
Term
 third quartile
Definition
 number that divides the bottom 75% from the top 25%
Term
 interquartile range (IQR)
Definition
 the difference between the first and third quartiles (Q3 - Q1)
Term
 Five-Number Summary
Definition
 min, Q1, Q2, Q3, max
Term
 outliers
Definition
 observations that fall well outside the overall pattern of data
Term
 lower limit
Definition
 Q1 -1.5 * IQR
Term
 upper limit
Definition
 Q3 + 1.5 * IQR
Term
 potential outliers
Definition
 observations that fall below the lower limit or above the upper limit
Term
 boxplot (box-and-whisker diagram)
Definition
 based on the five-number summary and can be used to provide a graphical display of the center and variation of a data set
Term
 constructing a boxplot procedure
Definition
 1. determine the quartiles2. determine potential outliers and the adjacent values3. draw a horizontal axis on which the numbers obtained in steps 1 and 2 can be located. above this axis, mark the quartiles and the adjacent values with vertical lines.4. connect the quartiles to make a box, and then connect the ox to the adjacent values with lines5. plot each potential outlier with an asterisk
Term
 whiskers
Definition
 two lines emanating from the box in a boxplot
Term
 population mean (mean of a variable)
Definition
 for a variable, x, the mean of all possible observations for the entire population
Term
 population standard deviation (standard deviation of a variable)
Definition
 for a variable, x, the standard deviation of all possible observations for the entire population
Term
 parameter
Definition
 a descriptive measure for a population
Term
 statistic
Definition
 a descriptive measure for a sample
Term
 standardized variable
Definition
 always has a mean of 0 and standard deviation of 1the standardized version of a variable x is obtained by first subtracting from x its mean and then dividing by its standard deviation
Term
 z-score
Definition
 for an observed value of a variable, x, the corresponding value of the standarized variable z is called the z-score of the observation. The term standard score is often used instead of z-score.A negative z-score indicates that the observation is below the mean, whereas a positive score indicates that the observation is above the mean
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