Statistics Exam 1 Flashcards

Sampling Methods

• Convenience Sampling: Gathering data by asking all students in a specific class, convenient but potentially biased.
• Simple Random Sampling: Involves randomly selecting individuals, similar to drawing cards from a shuffled deck.
• Cluster Sampling: Selecting a random classroom or room in a house to survey all students/items within that specific area.
• Stratified Sampling: Divides the population into subgroups (e.g., grade levels) and selects individuals from each subgroup to ensure representation.
• Systematic Sampling: Involves selecting every nth item from a list, such as every 15th phone number.

Statistical Measurements

• Central Tendency: Measures the "middle" or "average" of a dataset, including mean, median, and mode.
• Variability: Describes how spread out the data values are around the average.

Measures of Central Tendency

• Mean: Best used with symmetrical data, represents the arithmetic average and is influenced by extreme values.
• Median: Useful for asymmetrical data to minimize the effect of outliers, identifies the middle value when data is ordered.
• Mode: Refers to the most frequently occurring value in a dataset, useful in categorical data analysis.

Z-scores and Data Distribution

• Z-score: Indicates how many standard deviations a data point is from the mean, calculated using the formula z = (x - μ) / σ.
• Range Rule of Thumb: States that most data points lie within two standard deviations from the mean; values beyond this range are considered unusual.

Sample Space

• Sample Space: A comprehensive list of all possible outcomes in a statistical experiment.

Combinations and Permutations

• Permutation: Used when order matters, such as awarding different prizes or arranging letters (e.g., MATH).
• Combination: Used when order does not matter, such as selecting children for a picture or dealing cards from a deck.

Probability and Distributions

• Continuous Distribution: The probability is represented by the area under the density function curve.
• normalcdf Function: Calculates the probability of a dataset falling between two points.
• invNorm Function: Finds a specific data point based on a given probability threshold.

Application Examples

• Analyzing the number of ways to award multiple prizes or schedule events often involves calculating permutations.
• Selecting a subset from a larger group without regard to order involves combinations, applicable in various situations like group photos or card hands.