STAT 1.2

Ratio Level

quantitative data that can be ordered, differences between data entries are meaningful, and zero pt indicates the absence of something

Ordinal level

are qualitative data that can be arranged in a meaningful order, but calculations such as addition or division do not make sense

Discreate Data

are quantitative data that can take on ONLY particular values and are usually counts

Boiling points (on the Celsius scale) for various caramel candies

Calculations can be performed on boiling points because they are measurements, making these data quantitative. Temperatures are measurements, so the data are continuous. For the Celsius scale, a temperature of zero degrees is simply a placeholder and does not indicate the absence of heat. Therefore, data from the Celsius scale are always at the interval level of measurement.

Heights of men entering the U.S. Marine Corps are an example of which type of data?

Continuous

Lengths of time it takes for new light bulbs to burn out are an example of which type of data?

Continuous

The genres of the music performed at the 2013 Grammys

Despite the fact that you may have your own personal preference for specific genres of music, there is no standard order. Therefore, music genres are nominal data.

Suppose instead that you wish to know the number of students whose favorite pizza topping is sausage. Explain why this data value is not at the nominal level of measurement.

In the second scenario, the data value is a count of students who prefer sausage. This data value is quantitative, not qualitative, so it is not a label and would not be considered to be at the nominal level of measurement.

Numbers of houses in various neighborhoods in a city

Numbers of houses are discrete data because houses are counted in whole numbers. A house under construction is still a house.

Bank account numbers are an example of which type of data?

Qualitative

Months of the year are an example of which type of data?

Qualitative

A survey response to "Do you favor a flat tax?" 1) Yes 2) No

Qualitative Neither Continuous or Discrete Nominal

A questionnaire asks the respondent to identify his/her gender. The respondent is asked to fill in the appropriate number on a form. 1) Male 2) Female

Qualitative Neither Discrete or Continuous Nominal

You toss a coin and record "head" as 1 and "tail" as 2.

Qualitative Neither Discrete or Continuous Nominal

The seat numbers on your concert tickets, such as A23 and A24

Seat numbers are ordinal because there is a meaningful order to the data, namely, the position in the theater.

The top ten Spring Break destinations as ranked by MTV

Since the rankings cannot be meaningfully added or subtracted, the data must be qualitative. Qualitative data are neither discrete nor continuous. The rankings are in a specific order, so the data are at the ordinal level of measurement.

Temperatures in Fahrenheit of cities in South Carolina

Temperatures could be measured to any level of precision based on the thermometer used, so these are continuous data.

Finishing times for runners in the Labor Day 10K race

The amount of time it takes for each runner to run the race is quantitative since calculations performed on these data are meaningful. A finishing time is a measurement, therefore the data are continuous. Differences between finishing times are meaningful, and a time of zero represents the absence of racing. We could also say that Andrew finished the race in half of Peyton's time; thus, the data are at the ratio level of measurement

Numbers of elliptical machines in every YMCA in your state

The numbers of elliptical machines are counts, so these are discrete data.

Suppose all students in a statistics class were asked what pizza topping is their favorite. Explain why these data are at the nominal level of measurement.

These data are nominal because the data simply describe or label the different toppings of the pizza.

Nominal level

are qualitative data consisting of labels or names

Quantitative Data

consists of counts and mearsurements

Qualitative Data

consists of labels or descriptions of traits

The birth years of your classmates are collected. What level of measurement are these data?

Birth years can be ordered. It is also meaningful to subtract years to determine the difference in age. However, the year 0 A.D. does not mean the beginning of time. Therefore, birth years are at the interval level of measurement.

Colors contained in a box of crayons

Colors are labels, so these data are qualitative. Qualitative data are neither discrete nor continuous. There are many ways to order colors, such as alphabetically or based on the color spectrum. However, when discussing colors of crayons, order is not the primary factor, as opposed to data such as rankings, in which order is important. Therefore, the data are at the nominal level of measurement.

The numbers of each color of jelly beans in a jar (assuming they are all whole) are an example of which type of data?

Discrete

The numbers of red cars on various roads are an example of which type of data?

Discrete

Heights of doors

Heights are measurements and again, depending on the ruler, the heights could be measured to any level of precision, so they are continuous data.

Letter grades on a test are an example of which type of data?

Neither Continuous or Discrete

Genders are an example of which type of data?

Neither Continuous or Driscete

Colors of jelly beans in a jar are an example of which type of data?

Neither Discrete or Continuous

A supervisor must give a summary evaluation rating from among the choices given below: 1) Poor 2) Fair 3) Good 4) Very good 5) Excellent

Qualitative Neither Continuous or Discrete Ordinal

Five people are in a bakery waiting for service. Each person takes a ticket when they enter the bakery in order to determine when they will be served. The person with the lowest ticket number will be served next.

Qualitative Neither Discrete or Continuous Ordinal

Class sizes of various sections of college algebra at your university are an example of which type of data?

Quantitative

Heights of sunflowers in a garden are an example of which type of data?

Quantitative

The temperature in Celsius at different locations in an Italian city.

Quantitative Continuous Interval

The lifetimes of 100 five volt batteries is recorded.

Quantitative Continuous Ratio

The IQ scores of students at the local college.

Quantitative Discrete Interval

The number of French fries in each of 40 individual servings.

Quantitative Discrete Ratio

The number of emergency phone calls received each day for 3030 randomly selected days.

Quantitative Discrete Ratio

The number of people who quit smoking cigarettes each year for the last ten years.

Quantitative Discrete Ratio

The salaries of 80 randomly selected employees.

Quantitative Discrete Ratio

Rankings of the most popular paint colors for the season

Rankings are numeric but not measurements or counts, so these are qualitative data.

Shades of red paint in a home improvement store

Shades of paint are descriptions and cannot be measured, so these are qualitative data.

Consider the ages in whole years of US presidents when they were inaugurated. What level of measurement are these data?

The ages of US presidents are measurable, can be ordered, and an age of zero indicates the absence of life. Therefore, ages are at the ratio level of measurement. In contrast to Example 1.8, involving birth years, you can be twice as old as someone else.

Amount of red primary dye necessary to make one gallon of each shade of red paint

The amounts of dye needed are measured and therefore are quantitative data

Numbers of paint choices available at several stores

The numbers of paint choices must be counted, so they are quantitative data as well.

Interval Level

are quantitative data that can be arranged in a meaningful order, and differences between data entries are meaningful

Contnuous Data

are quantitative data that can take on any value in a given interval and are usually measurements