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Chapter 1. Introduction to Statistics. Data Classification [optional]. § 1.2. Types of Data. Data sets can consist of two types of data: qualitative data and quantitative data . Data. Quantitative Data. Qualitative Data. Consists of attributes, labels, or nonnumerical entries.

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types of data
Types of Data
  • Data sets can consist of two types of data: qualitative data and quantitative data.

Data

Quantitative Data

Qualitative Data

Consists of attributes, labels, or nonnumerical entries.

Consists of numerical measurements or counts.

qualitative and quantitative data

Qualitative data

Quantitative data

Qualitative and Quantitative Data
  • Example:
  • The grade point averages of five students are listed in the table. Which data are qualitative data and which are quantitative data?
levels of measurement

Lowest to highest

Levels of Measurement
  • The level of measurement determines which statistical calculations are meaningful. The four levels of measurement are: nominal, ordinal, interval,and ratio.

Nominal

Levels of Measurement

Ordinal

Interval

Ratio

nominal level of measurement
Nominal Level of Measurement
  • Data at the nominallevel of measurement are qualitative only.

Nominal

Calculated using names, labels, or qualities. No mathematical computations can be made at this level.

Levels of Measurement

Colors in the US flag

Names of students in your class

Textbooks you are using this semester

ordinal level of measurement
Ordinal Level of Measurement
  • Data at the ordinallevel of measurement are qualitative or quantitative.

Levels of Measurement

Ordinal

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

Top 50 songs played on the radio

interval level of measurement
Interval Level of Measurement
  • Data at the intervallevel of measurement are quantitative. A zero entry simply represents a position on a scale; the entry is not an inherent zero.

Levels of Measurement

Interval

Arranged in order, the differences between data entries can be calculated.

Temperatures

Years on a timeline

Atlanta Braves World Series victories

ratio level of measurement
Ratio Level of Measurement
  • Data at the ratiolevel of measurement are similar to the interval level, but a zero entry is meaningful.

A ratio of two data values can be formed so one data value can be expressed as a ratio.

Levels of Measurement

Ratio

Ages

Grade point averages

Weights

summary of levels of measurement

Level of measurement

  • Put data in categories
  • Arrange data in order
  • Subtract data values
  • Determine if one data value is a multiple of another
Summary of Levels of Measurement
  • Nominal
  • Yes
  • No
  • No
  • No
  • Ordinal
  • Yes
  • Yes
  • No
  • No
  • Interval
  • Yes
  • Yes
  • Yes
  • No
  • Ratio
  • Yes
  • Yes
  • Yes
  • Yes