anticipating patterns There may be some instances where we would like to combine two distributions together. For instance, if we are looking at the distribution of number of daughters and sons that families have. If we know the mean and standard deviation of two distribution, we can combine them to create a new distribution and calculate the mean and standard deviation of the new distribution.

anticipating patterns Probability: the long-term relative frequency of an outcome; the likelihood of something happening (real number between 0 and 1) Chance experiment: a planned operation carried out under controlled conditions, without a predetermined result (ex: flipping a coin) Outcome: the result of an experiment Sample space: the set of

anticipating patterns A discrete variable can only take a countable number of values. Each probability is a number from zero to one (including zero and one). The variable is random if the sum of the probabilities is one (See the image) Multiply each value by its probability and find the sum of the products.

anticipating patterns The central limit theorem states that we can start with any distribution (discrete or continuous) with a mean and standard deviation. If we continuously take larger and larger samples and calculate their means, the means will form a normal distribution. This tends to happen regardless of the type of distribution that we start with.

anticipating patterns Commonly seen in real life-thus called the "Normal" distribution The "bell curve" - symmetrical shape. Continuous distribution Mean and median are equal - data tends to be around this central value with no bias left or right. The more extreme a value is, the less often it appears (See the graph) We see the mean in the middle.

exploring data Level of measurement is the way that a set of data is measured. There are several scales: Nominal scale level: categorical / qualitative Ordinal scale level: numerical / quantitative Interval scale level: numerical / quantitative Ratio scale level: numerical / quantitative Remember: categorical data is the type of data that is not quantified.

exploring data There are two definitions of statistics: The science/practice of collecting, organizing, and analyzing numerical data A measurable characteristic of a sample. Ex: average height, average GPA, average income of a certain group Some key terms about statistics: Population: a collection of persons or things that can be studied.

exploring data Levels of measurement is the way that data is measured. Nominal scale level - categorical / qualitative Ordinal scale level - numerical / quantitative Ordinal scale is similar to nominal scale except it can be ordered. While it can be ordered, we can't measure differences between it.

sampling experimentation Sample study: estimating the value of a parameter for a population We take a sample from some population and compute statistics for it. We use those statistics in order to estimate parameters for that population. For example: compute the mean height of a hundred Americans Observational study: trying to understand the relationship between two variables in a population.

SAMPLING EXPERIMENTATION Generalizability of results means who can the results of a survey be applied to. Results of a survey can only be generalized to the population that the sample comes from. Bias can affect the generalizability of results and lead to an overestimate or underestimate.

statistical inference Estimation is processes used to make inferences about a population based on information from a sample. Sample statistics are used to estimate population parameters.

statistical inference Confidence intervals estimate a parameter We use the sample mean/proportion to estimate the population mean/proportion within a certain interval Hypothesis tests help us make decisions about a parameter Once we collect and analyze data, we will decide if there is sufficient evidence to make a claim about the parameter using the data.