Types of data

Parameter vs. StatisticParameter: Measured characteristic of a

population

Statistic: Measured characteristic of a sampleExamples: Which is a parameter and which is a statistic?Examples: Which is a parameter and which is a statistic?

In 1936, Literary Digest polled 2.3 million adults in the United States, and 57% said that they would vote for Alf Landon for the presidency.

There are exactly 100 Senators in the 109th Congress of the United States, and 55 of them are Republicans.

Parameter

Statistic

Determine which is a parameter and which is a statistic

When given the option 75% of the high school teachers, chose to work a day in the summer and have the day before Thanksgiving off.

50 girls from the freshman class were surveyed and 83% said they like the food better at the high school cafeteria than the middle school cafeteria.

54.7% of all the counties in Pa voted for Obama in the 2008 Presidential election.

100 students were randomly selected and found the amount of money they make an hour. The average hourly wage is $8.25.

Type of Parameters

Type of Statistics

•Quantitative Data: Data consisting of numbers representing counts or measurements

•Categorical Data: Data that can be separated into different categories that are distinguished by some nonnumeric characteristic

Examples: Determine which type data for each of the followingExamples: Determine which type data for each of the following

1) The political party affiliations (Democratic, Republican, Independent, other) of survey respondents.

2) The numbers 24, 28, 17, 54, and 31 are sewn on the shirts of the LA Lakers starting basketball team. These numbers are substitutes for names.

3) The ages (in years) of survey respondents.

Categorical Data

Categorical Data

Quantitative Data

•Discrete DataDiscrete Data: Data with the property that the number of possible values is either a finite number or a “countable” number, which results in 0 possibilities, or 1 possibility, or 2 possibilities, and so on

•Continuous Data:Continuous Data: Data resulting from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumpsExamples: Which is discrete data and which is continuous data?Examples: Which is discrete data and which is continuous data?

1) The numbers of eggs that hens lay.

2) The amount of milk from a cow.

Discrete Data

Continuous Data

Work with a partner: Come up with an example of discrete type of data and an example of a continuous type of data.

1) Nominal Level of Measurement: characterizes data that consist of names, labels, or categories only

• Example: Yes/No/Undecided – type of survey responses• Example: Political Party - the political party affiliation of survey

respondents

2) Ordinal Level of Measurement: characterizes data that may be arranged in order, but differences between data values either cannot be determined or are meaningless• Example: Course Grades – A high school teacher assigns grades

A, B, C, D, or E. These grades can be arranged in order but we can’t determine differences between the grades. (For example A is higher than B but you cannot subtract B from A)

• Example: Ranks – U.S. News and World Report ranks colleges

3) Interval Level of Measurement: characterizes data that can be arranged in order and for which differences between data values are meaningful• Like ordinal level of measurement but the difference between

any two data values is meaningful. • Data at this level DO NOT have a natural zero starting point. • Example: Temperatures – Body temperatures of 98.20 F and

98.60 F. These values can be ordered and you can find the difference between them

• Example: Years – the years 1492 and 1776

4) Ratio Level of Measurement: characterizes data that can be arranged in order, for which differences between data values are meaningful, and there is an inherent zero starting point• Like the interval level but this measurement has a natural zero • Example: Distances – Distances (in km) traveled by cars (0 km

represents no distance traveled, and 400 km is twice as far as 200 km)

• Example: Prices – Prices of college textbooks ($0 does represent no cost, and $100 book does cost twice as much as a $50 book.)