Chapter 3: Descriptive Statistics: Numerical Measures

Question 1

sample statistics

Answer 1

a numerical value used as a summary measure for a sample (ex. the sample mean, x bar, the sample variance, s^2, and the sample standard deviation, s)

Question 2

population parameter

Answer 2

a numerical value used as a summary measure for a population (ex. the population mean, u, the population variance, o^2, and the population standard deviation, o)

Question 3

point estimator

Answer 3

a sample statistic, such as x bar, s^2, and s, used to estimate the corresponding population parameter.

Question 4

mean

Answer 4

a measure of central location computed by summing the data values and dividing by the number of observations.

Question 5

median

Answer 5

a measure of central location provided by the value in the middle when the data are arranged in ascending order.

Question 6

mode

Answer 6

a measure of central location, defined as the value that occurs with greatest frequency.

Question 7

weighted mean

Answer 7

the mean obtained by assigning each observation a weight that reflects its importance.

Question 8

geometric mean

Answer 8

a measure of location that is calculated by finding the nth root of the product of n values.

Question 9

percentile

Answer 9

a value that provides information about how the data are spread over the interval from the smallest to the largest value

Question 10

pth percentile

Answer 10

for a data set containing n observations, the pth percentile divides the data into two parts: approximately p% of the observation are less that the pth percentile and approximately (100-p)% of the observations are greater than the pth percentile.

Question 11

quartiles

Answer 11

the 25th, 50th, and 75th percentiles, referred to as the first, second (median), and third quartile, respectively. the quartiles can be used to divide a data set into four parts, with each part containing approximately 25% of the data.

Question 12

range

Answer 12

a measure of variability, defined to be the largest value minus the smallest value.

Question 13

interquartile range (IQR)

Answer 13

a measure of variability, defined to be the difference between the third and first quartiles

Question 14

variance

Answer 14

a measure of variability based on the squared deviations of the data values about the mean.

Question 15

standard deviation

Answer 15

a measure of variability computed by taking the positive square root of the variance.

Question 16

coefficient of variation

Answer 16

a measure of relative variability computed by dividing the standard deviation by the mean and mulptiplying by 100

Question 17

skewness

Answer 17

a measure of the shape of a data distribution. data skewed to the left=negative skewness. skewed to the right=positive skewness. symmetrical data=zero skewness

Question 18

z-score

Answer 18

a value computed by dividing the deviation about the mean (xi-x bar) by the standard deviation s. a z-score is referred to as a standardized value and denotes the number of standard deviations xi is from the mean.

Question 19

chebyshev’s theorem

Answer 19

a theorem that can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean

Question 20

emperical rule

Answer 20

a rule that can be used to compute the percentage of data values that must be within one, two and three standard deviations of the mean for the data that exhibit a bell-shaped distribution.

Question 21

outlier

Answer 21

an unusually small or large data value

Question 22

five number summary

Answer 22

a technique that uses 5 numbers to summarize the data: smallest value, 1st quartile, median, 3rd quartile, largest value

Question 23

box plot

Answer 23

a graphical summary of data based on a 5 number summary

Question 24

covariance

Answer 24

a measure of linear association between two variables. positive values=positive relationship. negative values=negative relationship.

Question 25

correlation coefficient

Answer 25

a measure of linear association between two variables that takes on values between -1 and +1. values near +1 indicate a strong positive linear relationship. values near -1 indicate a strong negative linear relationship. and values near zero lack any liner relationship.

Question 26

a numerical value used as a summary measure for a sample (ex. the sample mean, x bar, the sample variance, s^2, and the sample standard deviation, s)

Answer 26

sample statistics

Question 27

a numerical value used as a summary measure for a population (ex. the population mean, u, the population variance, o^2, and the population standard deviation, o)

Answer 27

population parameter

Question 28

a sample statistic, such as x bar, s^2, and s, used to estimate the corresponding population parameter.

Answer 28

point estimator

Question 29

a measure of central location computed by summing the data values and dividing by the number of observations.

Answer 29

mean

Question 30

a measure of central location provided by the value in the middle when the data are arranged in ascending order.

Answer 30

median

Question 31

a measure of central location, defined as the value that occurs with greatest frequency.

Answer 31

mode

Question 32

the mean obtained by assigning each observation a weight that reflects its importance.

Answer 32

weighted mean

Question 33

a measure of location that is calculated by finding the nth root of the product of n values.

Answer 33

geometric mean

Question 34

a value that provides information about how the data are spread over the interval from the smallest to the largest value

Answer 34

percentile

Question 35

for a data set containing n observations, the pth percentile divides the data into two parts: approximately p% of the observation are less that the pth percentile and approximately (100-p)% of the observations are greater than the pth percentile.

Answer 35

pth percentile

Question 36

the 25th, 50th, and 75th percentiles, referred to as the first, second (median), and third quartile, respectively. the quartiles can be used to divide a data set into four parts, with each part containing approximately 25% of the data.

Answer 36

quartiles

Question 37

a measure of variability, defined to be the largest value minus the smallest value.

Answer 37

range

Question 38

a measure of variability, defined to be the difference between the third and first quartiles

Answer 38

interquartile range (IQR)

Question 39

a measure of variability based on the squared deviations of the data values about the mean.

Answer 39

variance

Question 40

a measure of variability computed by taking the positive square root of the variance.

Answer 40

standard deviation

Question 41

a measure of relative variability computed by dividing the standard deviation by the mean and mulptiplying by 100

Answer 41

coefficient of variation

Question 42

a measure of the shape of a data distribution. data skewed to the left=negative skewness. skewed to the right=positive skewness. symmetrical data=zero skewness

Answer 42

skewness

Question 43

a value computed by dividing the deviation about the mean (xi-x bar) by the standard deviation s. a z-score is referred to as a standardized value and denotes the number of standard deviations xi is from the mean.

Answer 43

z-score

Question 44

a theorem that can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean

Answer 44

chebyshev’s theorem

Question 45

a rule that can be used to compute the percentage of data values that must be within one, two and three standard deviations of the mean for the data that exhibit a bell-shaped distribution.

Answer 45

emperical rule

Question 46

an unusually small or large data value

Answer 46

outlier

Question 47

a technique that uses 5 numbers to summarize the data: smallest value, 1st quartile, median, 3rd quartile, largest value

Answer 47

five number summary

Question 48

a graphical summary of data based on a 5 number summary

Answer 48

box plot

Question 49

a measure of linear association between two variables. positive values=positive relationship. negative values=negative relationship.

Answer 49

covariance

Question 50

a measure of linear association between two variables that takes on values between -1 and +1. values near +1 indicate a strong positive linear relationship. values near -1 indicate a strong negative linear relationship. and values near zero lack any liner relationship.

Answer 50

correlation coefficient