Starter QUIZ Take scrap paper from little table Ask each student in this class if they are taking a foreign language class, record their answers and answer the following questions. 1) Name the population. 2) Name the sample. 3) Give a piece of data. 4) Is your data a parameter or a statistic? 5) Give an inferential statistic about the info you collected.

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Section 1.2 Objectives Distinguish between qualitative data and quantitative data Classify data with respect to the four levels of measurement 3 Larson/Farber 4th ed.

Types of Data Qualitative Data Consists of attributes, labels, or nonnumerical entries. MajorPlace of birth Eye color 4 Larson/Farber 4th ed.

Types of Data Quantitative data Numerical measurements or counts. AgeWeight of a letterTemperature 5 Larson/Farber 4th ed.

Larson & Farber, Elementary Statistics: Picturing the World, 3e 6 Types of Data Data sets can consist of two types of data: qualitative data and quantitative data. Data Qualitative Data Quantitative Data Consists of attributes, labels, or nonnumerical entries. Consists of numerical measurements or counts.

Example: Classifying Data by Type The base prices of several vehicles are shown in the table. Which data are qualitative data and which are quantitative data? (Source Ford Motor Company) 7 Larson/Farber 4th ed.

Solution: Classifying Data by Type Quantitative Data (Base prices of vehicles models are numerical entries) Qualitative Data (Names of vehicle models are nonnumerical entries) 8 Larson/Farber 4th ed.

Larson & Farber, Elementary Statistics: Picturing the World, 3e 9 Levels of Measurement The level of measurement determines which statistical calculations are meaningful. The four levels of measurement are: nominal, ordinal, interval, and ratio. Levels of Measurement Nominal Ordinal Interval Ratio Lowest to highest

Larson & Farber, Elementary Statistics: Picturing the World, 3e 10 Nominal Level of Measurement Data at the nominal level of measurement are qualitative only. Levels of Measurement Nominal Calculated using names, labels, or qualities. No mathematical computations can be made at this level. Colors in the US flag Names of students in your class Textbooks you are using this semester

Larson & Farber, Elementary Statistics: Picturing the World, 3e 11 Ordinal Level of Measurement Data at the ordinal level of measurement are qualitative or quantitative. Levels of Measurement Arranged in order, but differences between data entries are not meaningful. Class standings: freshman, sophomore, junior, senior Numbers on the back of each player’s shirt Ordinal Top 50 songs played on the radio

Levels of Measurement Nominal level of measurement Qualitative data only Categorized using names, labels, or qualities No mathematical computations can be made Ordinal level of measurement Qualitative or quantitative data Data can be arranged in order Differences between data entries is not meaningful 12 Larson/Farber 4th ed.

Larson & Farber, Elementary Statistics: Picturing the World, 3e 13 Interval Level of Measurement Data at the interval level of measurement are quantitative. A zero entry simply represents a position on a scale; the entry is not an inherent zero. Levels of Measurement Arranged in order, the differences between data entries can be calculated. TemperaturesYears on a timeline Interval Atlanta Braves World Series victories

Levels of Measurement Interval level of measurement Quantitative data Data can ordered Differences between data entries is meaningful Zero represents a position on a scale (not an inherent zero – zero does not imply “none”) 14 Larson/Farber 4th ed.

Larson & Farber, Elementary Statistics: Picturing the World, 3e 15 Ratio Level of Measurement Data at the ratio level of measurement are similar to the interval level, but a zero entry is meaningful. Levels of Measurement A ratio of two data values can be formed so one data value can be expressed as a ratio. AgesGrade point averages Ratio Weights

Levels of Measurement Ratio level of measurement Similar to interval level Zero entry is an inherent zero (implies “none”) A ratio of two data values can be formed One data value can be expressed as a multiple of another 16 Larson/Farber 4th ed.

Example: Classifying Data by Level Two data sets are shown. Which data set consists of data at the nominal level? Which data set consists of data at the ordinal level? (Source: Nielsen Media Research) 17 Larson/Farber 4th ed.

Solution: Classifying Data by Level Ordinal level (lists the rank of five TV programs. Data can be ordered. Difference between ranks is not meaningful.) Nominal level (lists the call letters of each network affiliate. Call letters are names of network affiliates.) 18 Larson/Farber 4th ed.

Example: Classifying Data by Level Two data sets are shown. Which data set consists of data at the interval level? Which data set consists of data at the ratio level? (Source: Major League Baseball) 19 Larson/Farber 4th ed.

Solution: Classifying Data by Level Interval level (Quantitative data. Can find a difference between two dates, but a ratio does not make sense.) Ratio level (Can find differences and write ratios.) 20 Larson/Farber 4th ed.

Larson & Farber, Elementary Statistics: Picturing the World, 3e 21 Summary of Levels of Measurement No YesNominal No Yes Ordinal NoYes Interval Yes Ratio Determine if one data value is a multiple of another Subtract data values Arrange data in order Put data in categories Level of measurement

Section 1.2 Summary Distinguished between qualitative data and quantitative data Classified data with respect to the four levels of measurement 22 Larson/Farber 4th ed.

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