Question

Fogle Enterprises, Inc uses statistics in its quality assurance program. In the table below are the important measurements used at some of Fogle Enterprises, Inc international warehouses. For each warehouse they have collected the following information: warehouse location, maximum inventory level in cases, amount of space in square footage, and the percent of humidity expressed as Extreme = e; High = h; moderate = m; or low = l.

City	Max Level	Square Foot	Humidity
Acapulco	99,000	7700.50	e
Bangkok	92,000	7800.00	m
Mexico City	77,000	5700.25	l
Montreal	72,000	5600.75	m
Paris	77,000	5800.00	h
Rome	88,000	6800.00	e
Toronto	78,000	6100.00	l

a. How many elements and how many variables are in this data set?

b. Identify the variables and indicate whether they are qualitative or quantitative.

c. What “scale of measurement” represents each of the variables?

d. Which variables are discrete or continuous, and why?

e. In the actual “SiP” what is the variable being measured and what is the scale of measurement?

Answer 1

a) There are 4 variables as mentioned in the question and they are as follows

i) Location

ii) Maximum inventory level in cases

iii) Amount of space in square footage

iv) Percentage of humidity

there are in all 7 elements as data is collcted for 7 different locations.

b) Qualitative variables are:

i) City

This is qualitative because this can't be measured in numbers.

ii) Humidity

This was initially quantitative but after converting it to extreme,high,moderate and low this became a qualitative variable.

Quantitative variables:

i) Maximum inventory level in cases

ii) Amount of space

These are quantitative because these can be measured in numbers.

c)

i) City-- nominal as it is just named variable

ii) Max level ---continuous scale because this does not have to be a specific value it changes as the city changes.

iii) Square foot ---- Square foot is the scale used to measure this variate.

iv) humidity --- ordinal scale.

d) Discrete variables

i) City is discrete as there can't be infinitely many options possible for this variate only a specific options are available.

ii) Humidity is a discrete variate as it takes only 4 values namely high, low, moderate and extreme.

Continuous variate

i) Max level is continuous as it can ideally take any value.

ii) Square foot is also continuous because this does not have any specific values to take as per the cities this would change.