Chapter 2: DataObjective: To go over an overview of Statistics and data

CHS Statistics

Overview of Statistics

Statistics – a collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data.

Let’s look at two different ways to interpret the definition: Statistics (the discipline) is a way of reasoning, along with

collection of tools and methods, designed to help us understand the world.

Statistics (plural) are particular calculations made from data.

Common misconceptions of statistics: Data are values with a context. (Datum is the singular form of

data). People often confuse these with statistics.

Think about it: Common advertisements such as, “Don’t drink and drive; you don’t want to be a statistic” are often incorrect. Can you find the mistake?

Population vs. Sample vs. Census

Population – the complete collection of all elements or subjects (scores, people, measurements, and so on) to be studied

Census – the collection of data from EVERY element in a population

Sample – a sub collection of elements drawn from a population

Examples:

Population Sample Census

Important Key Points Throughout Chapter 1

Sample data must be collected in an appropriate way, such as through a process of random selection.

If sample data are not collected in an appropriate way, the data are useless.

Population vs. Sample - You Decide!

In a recent survey, 1000 of the 7126 students of the Seneca Valley School District stated that they liked the idea of starting school after Labor Day.

 

a) What is the population?

b) What is the sample?

 

Data

Data (plural) – observations (such as measurements, genders, and survey responses) that have been collected

Datum (singular)

Sometimes used to find statistics if the context of the data is randomly selected and/or representative of the population

Parameter vs. Statistic

Parameter – a numerical measurement describing some characteristic of a population

Statistic – a numerical measurement describing some characteristic of a sample

Parameter vs. Statistic – YOU DECIDE!

1) A recent survey of a sample of MBAs reported that the average salary for an employee with an MBA is more than $82,000.

2) Starting salaries for the 667 MBA graduates of the University of Chicago Graduate School of Business increased 8.5% from the previous year.

3) In a random check of a sample of retail stores, the Food and Drug Administration found that 34% of the stores were not storing fish at the proper temperature.

4) When Lincoln was first elected to the presidency, he received 39.82% of the 1,865,908 votes cast.

Two Types of Data

Quantitative Data – values that answer questions about the quantity or amount (with units) of what is being measured. Examples: income ($), height (inches), weight (pounds)

Categorical Data – (qualitative data) can be separated into different categories that are often distinguished by some nonnumeric characteristic Examples: sex, race, ethnicity, zip codes

Wait? Hold up! Did I just see zip codes as categorical data? I thought they were numbers…

Categorical vs. Quantitative - You Decide!

Length of a song

Responses in an opinion poll

Telephone Number

 

Income of college graduates

The genders of college graduates

Discrete vs. Continuous Data

Discrete Data – result when a number of possible values is either a finite number or a “countable” number (dealing with counts) Example: the number of students with blonde hair

Continuous Data – result from infinitely many possible values that correspond to some continuous scale that covers a range of values without gaps, interruptions, or jumps (often times has units of measure attached) Example: the amount of rainfall in Zelienople this past

month

Discrete vs. Continuous Data – YOU DECIDE!

1) X represents the number of motorcycle accidents in one year in California.

2) x represents the length of time it takes to get to work.

3) x represents the volume of blood drawn for a blood test.

4) x represents the number of rainy days in the month of July in Orlando, Florida.

5) x represents the amount of snow (in inches) that fell in Nome, Alaska last winter.

Levels of Measurement

Nominal – characterized by data that consist of names, labels, or categories only The data cannot be arranged in an ordering scheme

(such as high to low)

Example: survey responses of yes, no, and undecided

Ordinal – can be arranged in some order, but the differences between the data values either cannot be determined or are meaningless Example: grade letters (A, B, C, D, F); movie ratings

(1, 2, 3, 4, 5) – while you can find the difference between the ratings, it is meaningless. The difference of 1 or 2 is meaningless, because it cannot be compared to other similar differences.

Levels of Measurement (continued)

Interval – similar to the ordinal level, but 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: temperatures (while 0° F seems like a good

starting point, it isn't necessarily)

Ratio –similar to the interval, but has a natural zero starting point (where zero indicates none of the quantity is present) Differences and ratios are meaningful

Example: weights of adult humans, prices of jeans

Levels of Measurement – YOU DECIDE!

1) Body temperature in degrees Fahrenheit of a swimmer

2) Collection of phone numbers

3) Final standing for the football Northeastern Conference

4) Heart rate (beats per minute) of an athlete.

Assignment

Chapter 2 Practice