EDA

• Experiment: Any process that generates a set of data.
• Sample Space: The set of all possible outcomes of a statistical experiment is represented by the symbol “S”.
• Element: Each outcome in a sample space is referred to as an element or a member of the sample space, or simply a sample point.
• The relationship between events and the corresponding sample space can be illustrated graphically by means of Venn diagrams.
• A ∩ B = regions 1 and 2, B ∩ C = regions 1 and 3, A ∪ C = regions 1, 2, 3, 4, 5, and 7, B’ ∩ A = regions 4 and 7, A ∩ B ∩ C = region 1, (A ∪ B) ∩ C’ = regions 2, 6, and 7.
• Sample Space with a Finite Number of Elements: If the sample space has a finite number of elements, they may be listed separated by commas and enclosed in braces.
• Sample Space of Possible Outcomes when a Coin is Flipped: The sample space S, of possible outcomes when a coin is flipped, may be written: S = {H, T}, where H and T correspond to heads and tails, respectively.
• Tree Diagram: In some experiments, it is helpful to list the elements of the sample space systematically by means of a tree diagram.
• The intersection of two events A and B, denoted by the symbol A ∩ B, is the event containing all elements that are common to A and B.
• The complement of an event A with respect to S is the subset of all elements of S that are not in A, denoted by the symbol A’.
• Given the sample space S = {t | t > 0}, where t is the life in years of a certain electronic component, the event A that the component fails before the end of the fifth year is the subset A = {t | 0 ≤ t < 5}.
• The union of the two events A and B, denoted by the symbol A∪B, is the event containing all the elements that belong to A or B or both.
• An event may be a subset that includes the entire sample space S or a subset of S called the null set φ, which contains no elements at all.
• Experiment with Two Flips: An experiment consists of flipping a coin and then flipping it a second time if a head occurs.
• Sample Space: The sample space S, of possible outcomes when a coin is flipped, may be written: S = {H, T}, where H and T correspond to heads and tails, respectively.
• Tree Diagram: If a tail occurs on the first flip, then a die is tossed once.
• Sample Space: The sample space S, of possible outcomes when a coin is flipped, may be written: S = {HH, HT, T1, T2, T3, T4, T5, T6}.
• Sample Space with a Large or Infinite Number of Sample Points: Sample spaces with a large or infinite number of sample points are best described by a statement or rule method.
• Sample Space: The sample space S, of possible outcomes when a coin is flipped, may be written: S = {x | x is a city with a population over 1 million}, which reads “S is the set of all x such that x is a city with a population over 1 million.”
• Sample Space: If S is the set of all points (x, y) on the boundary or the interior of a circle of radius 2 with center at the origin, we write the rule: S = {(x, y) | }.
• Events: For any given experiment, we may be interested in the occurrence of certain events rather than in the occurrence of a specific element in the sample space.
• Event: An event is a subset of a sample space.
• Descriptive statistics involves the collection, organization, summarization and presentation of data.
• Inferential statistics interprets and draws conclusions from the data.
• Measures of Central Tendency include Mean, median and mode.
• The Mean, also known as the arithmetic mean, is the most commonly used measure of central tendency.
• The standard deviation of a sample is represented by the Greek letter sigma (σ).
• The variance of a data set is the square of the standard deviation of the data.
• The standard deviation of a sample can also be represented by the Roman letter s (σ).
• The standard deviation of a sample is calculated by dividing the sum of the values in the sample by the number of values in the sample.
• To find the mean for a set of data, find the sum of the data values and divide by the number of data values.
• The range of a set of data values is the difference between the greatest data value and the least data value.
• The standard deviation uses the sum of the squares of deviations.
• The sum of all deviations is 0 for all set of data therefore we cannot use the sum of deviations as a measure of dispersion.
• The standard deviation of a set of numerical data makes use of the amount by which each individual data value deviates from the mean.
• For a population, the standard deviation is represented as σ.
• For a sample, the standard deviation is represented as σ.
• The mean of n numbers is the sum of the numbers divided by n.
• The median is the middle number or the mean of the two middle numbers in the list of numbers that have been arranged in numerical order from smallest to largest or largest to smallest (ranked list).
• The median is the point that separates the upper half from the lower half of the data.