what is statistics statistics is the study of how to collect, organize, analyze, and interpret data

WHAT IS STATISTICS STATISTICS is the study of how to collect, organize, analyze, and interpret data.


We could do a survey to COLLECT data about something we want to study or investigate.



We could then ORGANIZE the data into a pie chart, t – table, or graph.




Next we can look at the data using statistical measures and ANALYZE the data to see what it is telling us.





Lastly, we can INTERPRET the findings by possibly predicting future outcomes using those measures.





Lastly, we can INTERPRET the findings by possibly predicting future outcomes using those measures.

Stock brokers are constantly using statistics to help predict future prices of stocks and commodities.

WHAT IS STATISTICS There are some definitions we need to cover before we really begin.


INDIVIDUALS – people or objects included in the study.



VARIABLE – a characteristic about the individuals to be measured or observed.




For example, we could do a study about people who have successfully climbed Mount Everest.




For example, we could do a study about people who have successfully climbed Mount Everest.The INDIVIDUALS would be the actual people.




For example, we could do a study about people who have successfully climbed Mount Everest.The INDIVIDUALS would be the actual people.A VARAIABLE could be the age or height of the people.





QUANTITATIVE DATA – has a value or numerical measurement for which mathematical operations such as addition or averaging can be calculated.






QUALITATIVE DATA – describes an individual by placing them in a category or group.






QUALITATIVE DATA – describes an individual by placing them in a category or group.

Going back to our Mt. Everest climbers, their age or height is QUANTITATIVE, male or female is QUALITATIVE.

WHAT IS STATISTICS POPULATION DATA – the data are from EVERY individual of interest.


SAMPLE DATA – the data are from ONLY SOME of the individuals of interest.



Again if we look at the Mt. Everest climbers; POPULATION DATA would include every person who ever climbed Mt. Everest. SAMPLE DATA could be just those who have climbed in the past 5 years.




POPULATION PARAMETER – a numerical measure that describes an aspect of the population.





The proportion of males who have climbed Mt. Everest is a POPULATION PARAMETER.






SAMPLE STATISTIC – a numerical measure that describes an aspect of a sample






SAMPLE STATISTIC – a numerical measure that describes an aspect of a sample

The proportion of females in the last 5 years is a SAMPLE PARAMETER.

WHAT IS STATISTICS EXAMPLE # 1 :

Television station QUE wants to know the proportion of TV owners in Virginia who watch the station’s new program at least once a week. The station asks a group of 1,000 TV owners in Virginia if they watch the program at least once per week.



a) Identify the individuals and the variable of the study



a) Identify the individuals and the variable of the study- The individuals are the 1,000 TV owners surveyed



a) Identify the individuals and the variable of the study- The individuals are the 1,000 TV owners surveyed- The variable is the response does, or does not watch at least once per week




b) Do the data comprise a sample ? If it does, what is the underlying population ?




b) Do the data comprise a sample ? If it does, what is the underlying population ?- The data does comprise a sample.




b) Do the data comprise a sample ? If it does, what is the underlying population ?- The data does comprise a sample.- The underlying population is all TV owners in Virginia.





c) Is the variable qualitative or quantitative ?





c) Is the variable qualitative or quantitative ?- the variable is QUALITATIVE – the categories are DOES or DOES NOT watch the show






d) Identify a QUANTITATIVE variable.






d) Identify a QUANTITATIVE variable.- examples of possible answers include age or income.







e) Is the proportion of viewers in the sample who watch the new program at least once per week a statistic or parameter ?







e) Is the proportion of viewers in the sample who watch the new program at least once per week a statistic or parameter ?- it is a statistic, the proportion is computed from the sample data.

WHAT IS STATISTICS LEVELS OF MEASUREMENT


Nominal - data that consists of names, labels, or categories.



For example : Months of the year such as August, December, June, or May are all nominal data.




Ordinal – data that can be arranged in order but the differences between data values are meaningless.





For Example : In a group of 319 students, Kim is ranked 27th, Joey is ranked 52nd, and Rachel is ranked 77th where 1st is the highest rank .





For Example : In a group of 319 students, Kim is ranked 27th, Joey is ranked 52nd , and Rachel is ranked 77th

where 1st is the highest rank .

** Even though the ranking is numeric, the differences in rank are meaningless. The difference between Kim and Joey is 25 and between Joey and Rachel is 25. Kim and Joey could have a small gap between their GPA and Joey and Rachel could have a larger gap between their GPA. But they are still separated by 25 spots each.







Interval – applies to data that can be arranged in order AND the differences between data values are meaningful.

For Example : Body temperatures of trout in the Yellowstone River.









Ratio – data that can be arranged in order. Also, both differences between values and ratios of data values are meaningful. Data at this level has a true zero.










For Example : The length of trout swimming in Yellowstone River.










For Example : The length of trout swimming in Yellowstone River.

An 18” trout is three times larger than a 6” trout. We can perform mathematical operations on the data.

WHAT IS STATISTICS EXAMPLE # 2 : Describe the level of measurement for each statement.


a) The Senator’s name is Sam Wilson


a) The Senator’s name is Sam Wilson- this is a nominal level



b) The senator is 58 years old



b) The senator is 58 years old- ratio level. Notice that age has a meaningful zero. It makes sense to give age ratios. Sam is 2x older than

Mike.




Mike.

c) The years in which the senator was elected were 1998, 1994, and 2010




Mike.

c) The years in which the senator was elected were 1998, 1994, and 2010 - Interval level. Dates can be ordered, and the difference between dates have meaning.




Mike.

c) The years in which the senator was elected were 1998, 1994, and 2010 - Interval level. Dates can be ordered, and the difference between dates have meaning. - however, ratios do not make sense. The year 2000 is not twice as large as the year 1000.




Mike.


d) The senator’s total taxable income last year was $878,314.




Mike.


d) The senator’s total taxable income last year was $878,314. - ratio level. His salary is 10 times larger than someone who makes $87,831.40




Mike.



e) A survey conducted by the senator regarding his water bill had choices of strongly support, support, neutral, against, or strongly against.




Mike.



e) A survey conducted by the senator regarding his water bill had choices of strongly support, support, neutral, against, or strongly against.

- ordinal level. The choices can be ordered but there is no meaningful numerical difference between two choices.

what is statistics statistics is the study of how to collect, organize, analyze, and interpret data

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