155S1.3_3 Types of Data
MAT 155
Dr. Claude Moore
Cape Fear Community College
Chapter 1
Introduction to Statistics
1­1 Review and Preview
1­2 Statistical Thinking
1­3 Types of Data
1­4 Critical Thinking
1­5 Collecting Sample Data
Section 1­3 Types of Data
• Parameter a numerical measurement describing some characteristic of a population.
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Section 1­3 Types of Data
Key Concept
The subject of statistics is largely about using sample data to make inferences (or generalizations) about an entire population. It is essential to know and understand the definitions that follow.
Section 1­3 Types of Data
• Statistic a numerical measurement describing some characteristic of a sample.
population
sample
parameter
statistic
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155S1.3_3 Types of Data
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Section 1­3 Types of Data
Section 1­3 Types of Data
Two types of data are
Quantitative Data
and
Categorical Data
(or qualitative or attribute) .
Section 1­3 Types of Data
Quantitative data can further be described by distinguishing between discrete and continuous types.
Quantitative ﴾or numerical﴿ data consists of numbers representing counts or measurements.
Example: The weights of supermodels
Example: The ages of respondents
Categorical ﴾or qualitative or attribute﴿ data
consists of names or labels ﴾representing categories﴿
Example: The genders ﴾male/female﴿ of professional athletes
Example: Shirt numbers on professional athletes uniforms ­ substitutes for names.
Section 1­3 Types of Data
• Discrete data
result when the number of possible values is either a finite number or a ‘countable’ number (i.e. the number of possible values is
0, 1, 2, 3, . . .)
Example: The number of eggs that a hen lays
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155S1.3_3 Types of Data
Section 1­3 Types of Data
• Continuous (numerical) data
result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps
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Section 1­3 Types of Data
Levels of Measurement
Another way to classify data is to use levels of measurement. Four of these levels are discussed in the following slides.
Example: The amount of milk that a cow produces; e.g. 2.343115 gallons per day
Gallons represent volume which is continuous.
Section 1­3 Types of Data
1. Nominal level of measurement characterized by data that consist of names, labels, or categories only, and the data cannot be arranged in an ordering scheme (such as low to high)
Example: Survey responses yes, no, undecided
Section 1­3 Types of Data
2. Ordinal level of measurement involves data that can be arranged in some order, but differences between data values either cannot be determined or are meaningless
Example: Course grades A, B, C, D, or F
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155S1.3_3 Types of Data
Section 1­3 Types of Data
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Section 1­3 Types of Data
4. Ratio level of measurement
3. Interval level of measurement like the ordinal level, with the additional property that the difference between any two data values is meaningful, however, there is no natural zero starting point (where none of the quantity is present)
Example: Years 1000, 2000, 1776, and 1492
Section 1­3 Types of Data
Levels of Measurement
1. Nominal ­ categories only
2. Ordinal ­ categories with some order
3. Interval ­ differences but no natural starting point
4. Ratio ­ differences and a natural starting point
the interval level with the additional property that there is also a natural zero starting point (where zero indicates that none of the quantity is present); for values at this level, differences and ratios are meaningful
Example: Prices of college textbooks ($0 represents no cost, a $100 book costs twice as much as a $50 book)
Section 1­3 Types of Data
Recap
In this section we have discussed:
Basic definitions and terms describing data
Parameters versus statistics
Types of data ﴾quantitative and qualitative﴿
Levels of measurement
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155S1.3_3 Types of Data
16/8. Pedestrian Walk Buttons (statistic or parameter) In New York City, there are 3250 walk buttons that pedestrians can press at traffic intersections. It was found that 77% of those buttons do not work (based on data from the article “ For Exercise in New York Futility, Push Button,” by Michael Luo, New York Times).
Determine whether the given values are from a discrete or continuous data set. 16/14. Poll Results In the Literary Digest poll, Landon received 16,679,583 votes.
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16/12. Movie Gross (statistic or parameter) The author randomly selected 35 movies and found the amount of money that they grossed from ticket sales. The average (mean) is $ 123.7 million.
Determine whether the given values are from a discrete or continuous data set. 16/18. Blood Pressure When a woman is randomly selected and measured for blood pressure, the systolic blood pressure is found to be 61 mm Hg.
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155S1.3_3 Types of Data
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Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.
17/22. Types of movies ( drama, comedy, adventure, documentary, etc.)
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.
17/26. Measured amounts of greenhouse gases (in tons per year) emitted by cars listed in Data Set 16 in Appendix B
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.
17/28. Ranks of cars evaluated by Consumer’s Union
Identify the (a) sample and (b) population. Also, determine whether the sample is likely to be representative of the population.
17/32. AOL Survey America Online asked subscribers to respond to this question: “ Which slogan do you hate the most?” Responders were given several slogans used to promote car sales, and Volkswagon’s slogan received 55% of the 33,160 responses. The Volkswagon slogan was “ Relieves gas pains.”
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