describing and summarizing data of a variable

discreate variable

discrete variables are variables that take finite number of values

frequency distribution

frequency distribution visual summary that shows how often each value occurs in the dataset

what is the different type of frequency distribution

• absolute frequency: the raw count of observations

• relative frequency (percentage): the precent of observations for each value

• cumulative percentage: the total percent of observations that fall below or above a certain

continues variable

continues variables are variables that have infante amount of values

types of ways to measure continues variables

• discretization: grouping continues variables into “bins” to create relative frequency

• probability density function (PDF): describes the relative likelihood for a random variable to take on a given value

• cumulative density function (CDF): represents the probability that a variable takes less than or equal to the specific limit

measures of loction

• Mean: average value

• median: the exact middle value

• mode: the most frequent occurring value

measure of variability

• range: largest - smallest

• variance: measures how sped out a set of numbers is from the mean

• standard deviation: measure the average distance between individual data points

measure of shape

• skewness: measure distribution asymmetry

• Kurtosis: measures tail weight

normal distribution (z test)

the classic bell curve. Most data points cluster around the middle, while extreme values trail off evenly on both sides

t-distribution (t-test)

looks like a normal bell curve but fatter outer edges. Used when you have a small sample size, because small samples are more unpredictable and carry extra uncertainty

Chi-square distribution

Chi-square is an asymmetry curve that starts at zero and skews heavily towards one side. Use when counting categories instead of averages

F distribution

F distribution is a skewed curve used when comparing variances or spreads across groups. Used when comparing three or more group at once