Introduction to Statistics UNIT 3: STATISTICS Introduction to Statistics

Statistics is the science of learning from data. What is statistics? Statistics is the science of learning from data. 1) COLLECTING DATA 2) ANALYZING DATA 3) DRAWING CONCLUSIONS

How do We Use Statistics? Why Study Statistics? When we are interested in something, we just want to be able to explain it. It allows us make important decisions in science, health, business and public policy. We use statistics to study the past and possibly use it to predict future experiences. How do We Use Statistics?

Am I going to win the election? How do We Use Statistics?

Am I going to win the election? We will use statistics to help answer Bob’s question. A population is all individuals or items that belong to a group being studied. A census collects information about everyone in a population. What is Bob’s population? ALL VOTES!!!

Is he going to survey the entire population? What is bob going to do? As a starter, he needs to conduct a survey. A survey is a method of collecting information about a population. Is he going to survey the entire population? Bob has to choose a sample that must be selected randomly to represent the entire population. A sample is a group of individuals or items that represent a population from which they are taken.

Can bob’s survey be biased? If Bob surveys a sample that is highly likely going to vote for him, his survey will not represent the entire population. Bias occurs when the result of a survey does not represent the population.

How can bob choose a sample? 6) VOLUNTARY RESPONSE SAMPLE 5) CONVENIENCE SAMPLING 1) Simple Random Sample 2) SYSTEMATIC SAMPLE 3) STRATIFIED RANDOM SAMPLE 4) CLUSTER SAMPLING

1) Simple Random Sample You list each member of the population and use random numbers to decide who is in the sample. Each member of the population has an equal chance of being selected. This produces an unbiased sample which we hope is representative. However, it is not always an accurate representation of the population.

2) Systematic Sample POPULATION SAMPLE Every nth member of the population is selected. For example, from a population of 24, we want to have sample of 6. 24/6 = 4. We will pick every 4th person to create our sample. POPULATION SAMPLE

3) Cluster Sample The population is divided into clusters and a certain number of clusters is chosen at random. Every member of the cluster is part of the sample. For example: if you are doing a survey within the school, different departments might be clusters. If the clusters are different from each other, it can lead to bias.

4) Stratified Sample It seems like cluster sampling. The population is divided into many subgroups (i.e., gender, age, ethnicity, location) and a random sample is selected from each subgroup in proportion to its size in the population. Population of 24 16 males 8 females 1/4 1/4 4 males 2 females

5) Convenience Sample You ask people nearby or people who walk past at the school, a shopping mall. You do what is easy or convenient. The sample contains those members of the population from which data is most easily collected. Convenience samples are often biased in some way. People might participate in the survey because they have an interest in the question.

6) Voluntary Response Sample The sample contains members of the population who have chosen to respond to the survey. It might lead to a bias because only those who care strongly enough about the survey will respond; therefore, the results from the sample are not representative of the entire population.

ADVANTAGES & DISADVANTAGES OF SAMPLING TECHNIQUES

Time to play Go to kahoot.it

1) A high school Vice-Principal enters the cafeteria and randomly selects two tables. All students at those two tables are surveyed. 2) A school is divided into 4 groups by grade. There are 300 grade nines, 350 grade tens, 270 grade elevens and 320 grade twelves. Proportion of each group chosen  10%. Thirty grade nines are surveyed, 35 grade tens, 27 grade elevens and 32 grade twelves

3) Students from Mr. Bulut’s math class are given a survey assignment 3) Students from Mr. Bulut’s math class are given a survey assignment. Kyle goes home and surveys his immediate family only.