Chapter 3 Vocabulary

Question 1

Arithemetic mean

Answer 1

The arithmetic mean of a variable is computed by adding all the values of the
variable in the data set and dividing by the number of observations.

Question 2

Population arithmetic mean

Answer 2

The population arithmetic mean, μ, is computed using all the individuals in a population and is a parameter.

Question 3

Sample arithmetic mean

Answer 3

The sample arithmetic mean, x , is computed using sample data and is a statistic.

Question 4

Mean

Answer 4

Although other types of means exist, the arithmetic mean is generally referred to as the mean.

Question 5

Median

Answer 5

The median of a variable is the value that lies in the middle of the data when arranged in
ascending order.

Question 6

Resistant

Answer 6

A numerical summary of data is said to be resistant if extreme values (very large or small) relative to the data do not affect its value substantially.

Question 7

Mode

Answer 7

The mode of a variable is the most frequent observation of the variable that occurs in the data set.

Question 8

No mode

Answer 8

If no observation occurs more than once, we say the data have no mode.

Question 9

Bimodal

Answer 9

If a set of data has two values of the variable that occur with the most frequency, we say the
data set is bimodal.

Question 10

Multimodal

Answer 10

if a data set has three or more data values that occur with the highest frequency, the data
set is multimodal.

Question 11

Dispersion

Answer 11

is the degree to which the data are spread out.

Question 12

Range

Answer 12

The range, R, of a variable is the difference between the largest and smallest data value.

Question 13

Deviation about the Mean

Answer 13

For a population, the deviation about the mean for the ith observation is
xi – μ. For a sample, the deviation about the mean for the i-th observation is xi - x bar .

Question 14

Population standard deviation

Answer 14

The population standard deviation, σ, of a variable is the square root of the sum of squared deviations about the population mean divided by the number of observations in the population, N. That is, it is the square root of the mean of the squared deviations about the population mean.

Question 15

Sample standard deviation

Answer 15

The sample standard deviation, s, of a variable is the square root of the sum of squared deviations about the sample mean divided by the n – 1, where n is the sample size.

Question 16

Population variance

Answer 16

The population variance is the square of the population standard deviation and is denoted σ^2.

Question 17

Sample variance

Answer 17

The sample variance is the square of the sample standard deviation and is denoted s^2.

Question 18

Degrees of freedom

Answer 18

For the sample standard deviation, this refers to the fact that we divide by n – 1 to compute standard deviation rather than n. We call n – 1 the degrees of freedom because the first n – 1 observations have freedom to be whatever value they wish, but the nth value has no freedom. It must be whatever value forces the sum of the deviations about the mean to equal zero.

Question 19

Bias

Answer 19

Whenever a statistic consistently underestimates a parameter, it is said to be biased.

Question 20

The Empirical Rule

Answer 20

f a distribution is roughly bell shaped, then (a) Approximately 68% of the data will lie within 1 standard deviation of the mean. (b) Approximately 95% of the data will lie within 2 standard deviations of the mean. (c) Approximately 99.7% of the data will lie within 3 standard deviations of the mean.

Question 21

Weighted mean

Answer 21

The weighted mean of a variable is found by multiplying each value of the variable by its corresponding weight, adding these products, and dividing this sum by the sum of the weights.

Question 22

z‐score

Answer 22

The z‐score represents the distance that a data value is from the mean in terms of the number of standard deviations.

Question 23

kth percentile

Answer 23

The kth percentile, denoted Pk, of a set of data is a value such that k percent of the observations are less than or equal to the value.

Question 24

Quartiles

Answer 24

divide data sets into fourths, or four equal parts.

Question 25

Interquartile range

Answer 25

The interquartile range, IQR, is the range of the middle 50% of the observations in a data set. That is, the IQR is the difference between the first and third quartiles and is found using the formula IQR = Q3 – Q1.

Question 26

Describe the distribution

Answer 26

Describe the distribution means to describe its shape (skewed left, skewed right, symmetric), its center (mean or median), and its spread (standard deviation or interquartile range).

Question 27

Outlier

Answer 27

An outlier is an extreme observation in a data set.

Question 28

Fences

Answer 28

Fences serve as cutoff points for determining outliers.

Question 29

Five‐number summary

Answer 29

The five‐number summary of a set of data consists of the smallest data value, Q1, the median, Q3, and the largest data value.

Question 30

Boxplot

Answer 30

Graphical summary of quantitative data used to identify shape of a distribution and outliers.

Question 31

Whiskers

Answer 31

The lines drawn from Q1 to the smallest data value that is larger than the lower fence and from Q3 to the largest data value that is smaller than the upper fence in a boxplot.