Statistics

Chapter 1: Introduction to Statistics

1. Definition: statistics is the science of planning studies and experiments and collecting data, organizing, summarizing, presenting, analyzing and interpreting data, and then drawing conclusions based on them.

2. Definition: Data are observations that have been collected.

   1. types of data:

      1. Quantitative: a number (age,weight,cost)

      2. Qualitative: a category/words (gender, car type, color of your shoes)

3. Definition: a population is a complete collection of all elements under study

   1. Notation: N= total population size

4. Definition: a parameter is a numerical measurement calculated from the population data

5. Definition: a sample is a subcollection of our population

6. Definition: a statistic is a numerical measurement calculated from out sample data

   1. types of quantitative data:

      1. discrete: a number that dosen’t involve a decimal or fraction

         1. ex. the number of…..

      2. continues: a number that can involve a decimal/ fraction

         1.  ex. the amount of or how much

7. Data can be:

   1. descriptive: presented in words pictures, or graphs

   2. inferential: presented using standard numeric symbols

8. levels of measurement for data

   1. nominal: categories only. no inherent order (qualitative)

      1. ex. favorite color

   2. ordinal: leveled/order data. order exists (qualitative)

      1. ex. low risk or high risk

   3. interval: ordered with no true zero.

      1. ex. temperature, time

   4. ratio: ordered with true zero

      1. ex. weight, amount of gas in your car

9. data collection method:

   1. two methods of collecting data:

      1. observational studies: observe facts and draw conclusions

      2. experiment: apply a treatment in a controlled environment to determine a response/outcome to the treatment

10. methods of sampling: sampling methods are different ways to collect a sample from a population

    1. simple random sampling: a sample of N is chosen so that every element in the population has an equal chance of being selected in the sample

       1. ex. picking names from a hat, picking cards from a box

    2. systematic sampling: select a starting point then pick every k element in the population

       1. ex. choosing every 10th customer that enters a store, selecting every 23rd order made for a given product

    3. convenance sampling: select elements from a population which are easiest to get

       1. ex. asking people in the math learning center if they love math and making a conclusion about how many people love math at MNSU

    4. stratified sampling: breaking population up into meaningful subgroups called strata, then drawing a simple random sample from each stratum

       1. ex.

    5. cluster sampling: dividing population into diverse clusters and randomly selecting some clusters (include all elements of those clusters)

       1. ex. a university randomly selects 5 dorms and surveys every student living in the dorm

    6.