PROBLEM -1
For each of the following variables, determine whether the variable is categorical or numerical. If the variable is numerical, determine
whether the variable is discrete or continuous.
a. Average bill amount paid to an Internet service provider
b. Mall store used most frequently for holiday shopping
c. Number of cars purchased during the person's lifetime
d. Day in which the person does the most holiday shopping (weekday, Saturday, Sunday)
a. To determine what kind of variable this is, first determine whether it is a categorical variable or a numerical variable.
Categorical variables (also known as qualitative variables) have values that can only be placed into categories such as yes and no.
Gender (male or female) is a categorical variable. So, too is "Do you shop online?" (yes or no).
Numerical variables (also known as quantitative variables) have values that represent a counted or measured quantity.
Average bill amount paid to an Internet service provider is a numerical variable because the variable has values that are numerical
quantities.
Numerical variables are further identified as discrete or continuous variables.
Discrete variables have numerical values that arise from a counting process. "Number of items purchased" is a discrete numerical variable
because its values represent the count of the number of items purchased.
Continuous variables have numerical values that arise from a measuring process. "The time spent waiting on a checkout line" is an
example of a continuous numerical variable because its values can represent a measurement with a stopwatch. Values of a continuous
variable can take on any value within a continuum or an interval, depending on the precision of the measuring instrument.
Average bill amount paid to an Internet service provider is a continuous numerical variable because the variable would be measured, not
counted.
Thus, average bill amount paid to an Internet service provider is a continuous numerical variable.
b. Mall store used most frequently for holiday shopping is categorical because the responses can only be placed into
categories.
Thus, mall store used most frequently for holiday shopping is a categorical variable.
c. Number of cars purchased during the person's lifetime is numerical because the variable has values that are numerical
quantities.
Number of cars purchased during the person's lifetime is a discrete numerical variable because the variable would be counted, not
measured. Thus, number of cars purchased during the person's lifetime is a discrete numerical variable.
d. Day in which the person does the most holiday shopping is categorical because the responses can only be placed into
categories.
Thus, day in which the person does the most holiday shopping is a categorical variable.
PROBLEM – 2
The table below contains data about the cost of electricity during a recent month for a random sample of 30 one-bedroom apartments
in a large city. Complete parts (a) through (c) below.
93 160 141 93 108 171 183 151 161 121
205 92 211 152 182 175 116 177 154 153
147 173 124 129 114 101 110 126 141 133
a. Construct a frequency distribution and a percentage distribution that have class intervals with the upper-class
boundaries $99, $119, and so on.
First organize these costs as an ordered array. An ordered array arranges the values of a numerical variable in rank order, from the
For each of the following variables, determine whether the variable is categorical or numerical. If the variable is numerical, determine
whether the variable is discrete or continuous.
a. Average bill amount paid to an Internet service provider
b. Mall store used most frequently for holiday shopping
c. Number of cars purchased during the person's lifetime
d. Day in which the person does the most holiday shopping (weekday, Saturday, Sunday)
a. To determine what kind of variable this is, first determine whether it is a categorical variable or a numerical variable.
Categorical variables (also known as qualitative variables) have values that can only be placed into categories such as yes and no.
Gender (male or female) is a categorical variable. So, too is "Do you shop online?" (yes or no).
Numerical variables (also known as quantitative variables) have values that represent a counted or measured quantity.
Average bill amount paid to an Internet service provider is a numerical variable because the variable has values that are numerical
quantities.
Numerical variables are further identified as discrete or continuous variables.
Discrete variables have numerical values that arise from a counting process. "Number of items purchased" is a discrete numerical variable
because its values represent the count of the number of items purchased.
Continuous variables have numerical values that arise from a measuring process. "The time spent waiting on a checkout line" is an
example of a continuous numerical variable because its values can represent a measurement with a stopwatch. Values of a continuous
variable can take on any value within a continuum or an interval, depending on the precision of the measuring instrument.
Average bill amount paid to an Internet service provider is a continuous numerical variable because the variable would be measured, not
counted.
Thus, average bill amount paid to an Internet service provider is a continuous numerical variable.
b. Mall store used most frequently for holiday shopping is categorical because the responses can only be placed into
categories.
Thus, mall store used most frequently for holiday shopping is a categorical variable.
c. Number of cars purchased during the person's lifetime is numerical because the variable has values that are numerical
quantities.
Number of cars purchased during the person's lifetime is a discrete numerical variable because the variable would be counted, not
measured. Thus, number of cars purchased during the person's lifetime is a discrete numerical variable.
d. Day in which the person does the most holiday shopping is categorical because the responses can only be placed into
categories.
Thus, day in which the person does the most holiday shopping is a categorical variable.
PROBLEM – 2
The table below contains data about the cost of electricity during a recent month for a random sample of 30 one-bedroom apartments
in a large city. Complete parts (a) through (c) below.
93 160 141 93 108 171 183 151 161 121
205 92 211 152 182 175 116 177 154 153
147 173 124 129 114 101 110 126 141 133
a. Construct a frequency distribution and a percentage distribution that have class intervals with the upper-class
boundaries $99, $119, and so on.
First organize these costs as an ordered array. An ordered array arranges the values of a numerical variable in rank order, from the
