Presentation on theme: "Section 2.1 ~ Data Types and Levels of Measurement"— Presentation transcript:
1 Section 2.1 ~ Data Types and Levels of Measurement Introduction to Probability and StatisticsMs. Young
2 Objective Why is this important? Sec. 2.1ObjectiveTo be able to classify data as qualitative or quantitative, to identify quantitative data as discrete or continuous, and to assign data at a level of measurement (nominal, ordinal, interval, or ratio).Why is this important?Learning how to classify the data will help us in later chapters with summarizing and displaying the data. It is very important to give a representative display of the data to avoid misconceptions.
3 Data Types Two basic types: qualitative and quantitative Sec. 2.1Data TypesTwo basic types: qualitative and quantitativeQualitative (categorical) data – values that can be placed in non-numerical categoriesExamples ~ eye color, ice cream flavors, car models, ratings (movie ratings, letter grades, pain scale ratings, etc.), social security numbers, etc.Numbers that wouldn’t be used for computations would be considered qualitativeQuantitative data – consist of values representing counts or measurementsExamples ~ times of runners in a race, incomes of college graduates, the number of students in different classes, temperature, etc.
4 Sec. 2.1Example 1Classify each of the following sets of data as either qualitative or quantitativeBrand names of shoes in a consumer surveyQualitative; brands are categoricalScores on a multiple choice examQuantitative; the numbers represent a count of how many questions were rightLetter grades on an essay assignmentQualitative; letter grades categorize based on ability levelNumbers on uniforms that identify basketball playersQualitative; the numbers identify the player, but wouldn’t be used to make computations
5 Quantitative Data Can be classified as either continuous or discrete Sec. 2.1Quantitative DataCan be classified as either continuous or discreteContinuous data – data that can take on any value in a given intervalCan be part of a whole numberExamples ~Weight; someone can weigh lbsTime; the time can be part of an hour (12:48 pm)Distance; length can be measured in parts (2.36 miles)Money; can be part of a dollar ($5.84)
6 Quantitative Data Cont’d.. Sec. 2.1Quantitative Data Cont’d..Discrete data – data that can take on only particular values and not others in-betweenExamples ~Number of students (whole numbers only)Shoe sizes (whole and half sizes only)Number of times a student took their driver’s test (whole numbers only)
7 Sec. 2.1Example 2For each data set, indicate whether the data are discrete or continuousMeasurements of the time it takes to walk a mileContinuousThe numbers of calendar years (such as 2007, 2008, 2009, etc.)DiscreteThe numbers of dairy cows on different farmsThe amounts of milk produced by dairy cows on a farm
8 Qualitative Levels of Measurement Sec. 2.1Qualitative Levels of MeasurementA level of measurement is a further classification of qualitative or quantitative dataQualitative (categorical) data can be classified further as either nominal or ordinalNominal level of measurement – characterized by data that consist of names, labels, or categories only; cannot be ranked or orderedExamples ~ eye color, ice cream flavors, jersey numbers, and gender of animalsOrdinal level of measurement – qualitative data that can be arranged in some order (such as low to high or high to low)Examples ~ star ratings of movies, pain level ratings, letter grades on a test, etc.“Time out to Think” on P.56
9 Quantitative Levels of Measurement Sec. 2.1Quantitative Levels of MeasurementQuantitative (numerical) data, whether it’s discrete or continuous, can be further classified as interval or ratioInterval level of measurement – applies to quantitative data in which intervals (difference) are meaningful and ratios (which involve division) are notData at this level have do not have a “true” zero pointExample ~ Temperature;Intervals (differences) are meaningful - 81˚F is hotter than 80˚F by the same amount that 28˚F is hotter than 27˚FRatios (division) are not meaningful - 20˚F is not twice as hot as 10˚F because it’s zero point (0˚F) does not represent a state of “no heat”
10 Quantitative Levels of Measurement Cont’d… Sec. 2.1Quantitative Levels of Measurement Cont’d…Ratio level of measurement – applies to quantitative data in which both intervals and ratios are meaningfulData at this level have a true zero pointExample ~ Walking distance;Intervals (differences are meaningful) - 10 miles is further than 5 miles by the same amount that 20 miles is further than 15Ratios (division) are meaningful - 10 miles really is twice as far as 5 miles because there is a true zero when it comes to distanceOther examples that would be classified as a ratio level of measurement include, but are not limited to, weights, speeds, and incomes
11 Sec. 2.1Example 3Identify the level of measurement for each of the following sets of dataNumbers on uniforms that identify players on a basketball teamNominal; the numbers are not numerically significant making these data qualitative and furthermore, the order is not meaningful. A player with the number 10 is not necessarily any better than a player with the number 3 on their jerseyStudent rankings of cafeteria food as excellent, good, fair, or poorOrdinal; there is no numerical significance and the categories are ranked from high to lowCalendar years of historical events, such as 1776, 1945, or 2001Interval; this is quantitative because the numbers are meaningful, but they are only meaningful when it comes to differences. They are not significant at the ratio level because there is no “true” zero. The year 0 is not the beginning of time
12 Sec. 2.1Example 3 Cont’d…Identify the level of measurement for each of the following sets of dataTemperatures on the Celsius scaleInterval; the differences are meaningful, but ratios are not. There is no “true” zero point – 0 degrees Celsius does not represent a state of no heat. It would not be appropriate to say that -40 degrees Celsius is twice as cold as -20 degrees Celsius.Runners’ times in the Boston MarathonRatio; time has a true zero. A time of 0 hours is the start of the race and it would be meaningful to say that 6 hours really is twice as long as 3 hours.
13 Summary Sec. 2.1 Data can be classified as qualitative or quantitative Qualitative data can be classified as nominal or ordinalQuantitative data can be classified as discrete or continuous and further as interval or ratioQualitativeQuantitativeNominalOrdinalDiscreteContinuousIntervalRatio