Introduction to Statistics: What is statistics?: Is the science of the collection of data , presentation/description of data, and finally the analysis/interpretation of a sample especially for drawing conclusion about the population from a sample .
Elementary Definitions: Population: is all individuals we wish to study. This could be collected data on US men and collecting data on their heights. This is near impossible to do, so we take out a sample.
Sample: Is a subset of the population. Our goal is to use that sample to draw a conclusion about the population. If we sample,we want to sample at random.
Inferential Statistics: It has the word "infer" in it. Inferential statistics tries to "infer" or draw a conclusion about the population based off the sample drawn. Before we draw a conclusion about the population based off the sample, we want to make sure our sample is A-OK. We do this by describing the sample somehow. This is where descriptive statistics comes into play.
Descriptive Statistics: Describes our sample to make sure it is A-OK. This is necessary before we do inferential statistics to draw a conclusion about the population based off the sample drawn. How do we use descriptive statistics where we are exploring our sample: 1) Outlier: we want to look for outliers which are usually large or unusually small values relative to the data in our sample. 2) Measures of center: mean, median 3) Measures of spread(variability): variance, standard deviation, quartiles 4) Measures of shape: we want to see if our sample data appear normal or skewed. INSERT DRAWINGS HERE!!!!!!!!!!! In skewed distributions the mean and median are different. 1) Histogram We use these two graphs to determine if the 2) Scattered plot graph is normal or skewed.
Individuals of a Dataset, Categorial Variables, and Quantitative Variables: Individuals: People are objects that we sampled. In this case it is US citizens.
Variables: Characteristics or attributes that describe the sampled individuals. Gender (1=male, 2=female), height (in), weight (Ibs), car type
Example 2: Let's say we collected data on trucks and recorded data on it weight(Ibs), color, age (years). a) What are the individuals? The individual are trucks since that is what we are sampling. b) What are the variables? The weight, color, and age.
Quantitative Variable: A variable in which finding the average makes sense to do. Height and weight is quantitative. Another sign a variable is quantitative is it has units of measure such as inches or pounds.
Categorical (qualitative): a variable in which finding the average does not make sense to do. For example gender and color is categorial. Categorical variables only have labels assigned to th