Statistics Section 1.1-1.4

Statistics

Study of Procedures for collecting, describing, and drawing conclusions from information

Statistics requires investigative process, 4 steps?

Formulate questions, Collect data, describe the data, draw conlusions.

Population

Entire Collection of individuals about which information is sought

Sample

Subset of a population, containing the individuals that are actually observed

Simple random sampling

Size n is a sample chosen by method in which each collection of n population items is equally likely to make up the sample, just as in a lottery

Stratified Sampling

population divided into groups called strata, where the members of each stratum are similar in some way, then a simple random sample is drawn from each stratum. Ex; One stratum would consist of full time employees while the other is part time employees.

Cluster

Drawn from the population in group or clusters. Used by U.S government agencies to measure income and unemployment

Voluntary Response

Used by the media to try to engage the audience; Ex: social media influencer might prompt followers to post comments or ask them to submit their thoughts through an online poll.

Sample of Convenience

sample that is not drawn by a well- defined random method

Statistic and Parameter

Easy way to remember these terms is that “statistic” and “sample” both begin with “s” and “parameter” and “population” both begin with “p”

Ex: Which of the following is a statistic and which is a parameter?

a. 57% of the teachers at Central High School are female

b. In a sample of 100 surgery patients who were given a new pain reliever, 78% of them reported significant pain relief

Answers: a. The number 57% is a parameter because it describes the entire population of teachers in the school

b. The number 78% is a statistic because it describes a sample. `

Qualitive Variables

Classify individuals into categories other words; descriptions; name of favorite song, Genres of Monday night TV shows

Quantitive variables

Tell how much or how many of something there is other words; counts or measurements; seating capacity of an auditorium

Discrete variables

possible values can be listed; 0, 1, 2 (whole numbers)

Continous Variables

take on any value within some interval; such as height can be 68, 68.1, 68.1452389 (not restricted)

Ordinal Variables

Qualitive Variables whose categories have natural ordering; A.B,C, D, E

Ex: small, medium, large

Nominal Variables

Qualitive Variables whose categories have no natural ordering

Ex: State of residence, gender

A ___is a subset of a ___ containing the individuals that are actually observed

Sample, population

Analogous to a Lottery

A Simple random sample

Ordinal

Ex;A car rental company has compact, mid size, and full size cars available

I got an A in statistics, a B in biology and C in history

Ratio

Number of classes a person is taking, number of siblings you have

Discrete data

The number of people visiting a museum each day

Ratio

Has the ratio level of measurement if zero represents the absence of the quantity and ratios are meaningful

Interval

If a value of zero does not indicate that none of the quantity is present

Systemic Sampling

Population items are ordered ex: Imagine walking alongside a line of people and choosing every third person.

SImple random sample on T-84

21—>math rnand, enter

then you press math over to prob and go down tyto randIntNoRep click enter.

Put in values of the numbers its asking for example in a class of 5; I’d put 1-5 so between those is my sample.

Relative Frequency

Relative Frequency = Frequency/ Sum of all frequencies

Lower class limit;

smallest value that can appear in the class

Upper Class limit;

Largest value of the class limit

using the data in table 2.7 construct a frequency distribution with classes of width 0.5

Class width = Largest data-smallest data/ number of classes

Skewed

a histogram is one side or tail is longer than the other.

• Skewed to the right is positive

• Skewed to the left is negative g

Midpoint

Class midpoint= Lower limit + Lower limit of next class/2