Midterm Review Flashcards
The science of collecting, organizing, presenting, analyzing, and interpreting data to make more informed decisions.
Statistics
Example: Statistical analysis helps businesses make data-driven decisions.
A measure of the likelihood that an event will occur.
Probability
Example: The probability of flipping a coin and getting heads is 0.5.
A variable whose possible values are numerical outcomes of a random phenomenon.
Random Variable
Example: The outcome of rolling a die is a random variable.
Describes how probabilities are distributed over the values of the random variable.
Probability Distribution
Example: The normal distribution describes probabilities of continuous outcomes.
Statistical measures that describe the main features of a collection of data in quantitative terms.
Descriptive Statistics
Example: Mean and standard deviation are common descriptive statistics.
The probability distribution of a given statistic based on a random sample.
Sampling Distribution
Example: Sampling distribution of the mean estimates the population mean.
A range of values, derived from sample statistics, that is likely to contain the value of an unknown population parameter.
Confidence Interval
Example: A confidence interval of [20, 30] suggests the population mean is likely within this range.
The method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis about the population.
Hypothesis Testing
Example: Hypothesis testing is used to determine if a new drug is effective.
The statement that there is no effect or no difference, and it serves as the default assumption to be tested.
Null Hypothesis
Example: Null hypothesis states there is no difference in test scores between two groups.
The probability of observing test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct.
P-Value
Example: A p-value of 0.03 indicates a 3% chance of obtaining the observed results if the null hypothesis is true.
A statistical measure that defines a value’s relationship to the mean of a group of values, measured in terms of standard deviations from the mean.
Z-Score
Example: A z-score of -1.5 indicates the value is 1.5 standard deviations below the mean.
The statistical theory that states that, given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.
Central Limit Theorem
Example: The central limit theorem allows for the use of normal distribution approximation in many statistical analyses.
True or False: In a normal distribution, 95% of the data lies within 1.96 standard deviations of the mean.
True
Example: Empirical rule states that in a normal distribution, approximately 95% of the data lies within 1.96 standard deviations of the mean.
Which measure is resistant to outliers?
A. Mean
B. Variance
C. Standard Deviation
D. Median
Median
Example: The median is often preferred over the mean when dealing with skewed data.
A set of all possible outcomes of an experiment.
Sample Space
Example: The sample space of rolling a die is {1, 2, 3, 4, 5, 6}.
True or False: The mode is the most frequent value in a dataset.
True
Example: In the dataset {2, 3, 3, 5, 7}, the mode is 3.
What type of variable can take any value within a range?
Continuous Variable
Example: Height, weight, and temperature are examples of continuous variables.
The difference between the 0.25 and 0.75 quantiles.
Interquartile Range (IQR)
Example: The IQR is used to measure the spread of the middle 50% of a dataset.
Which of the following is a discrete probability distribution?
A. Binomial distribution
B.Normal Distribution
C. Exponential Distribution
A. Binomial Distribution
Example: The binomial distribution models the number of successes in a fixed number of trials.
The event that either or both events occur.
Union of two events
Example: The union of rolling an even number and rolling a prime number on a die is the event {2, 3, 4, 5, 6}.
Probability based on observed data or past experiences.
Empirical Probability
Example: The empirical probability of drawing a red card from a deck of cards is based on past observations.
What is the probability of rolling a 3 on a fair six-sided die?
1/6
Example: The probability of rolling a 3 on a fair die is 1/6 or approximately 16.67%.
The measure of the likelihood of an event occurring given that another event has already occurred.
Conditional Probability
Example: The conditional probability of drawing a red card given that a heart has already been drawn.
Which statistical measure is used to quantify data spread?
A. Mean
B. Standard Deviation
C. Mode
B. Standard Deviation
Example: Standard deviation measures the dispersion of data points around the mean.
