Statistics Cheat Sheet PDF

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Chapter 1:

Chapter 2:

Statistics: is the science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions. There are two types of statistics. Descriptive statistics: are procedures used to organize and summarize data. Inferential statistics: involves taking a sample from a population and making estimates about a population based on the sample results. A population: is an entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest. A sample: is a part of the population. A qualitative variable: is categorical or nonnumeric. Usually, we are interested in the number or percent of the observations in each category. Qualitative data are usually summarized in graphs and bar charts. quantitative variables: Discrete variables can assume only certain values, and there are usually gaps between values. continuous variable can assume any value within a specified range. four levels of measurement: 1. With the nominal level, the data are sorted into categories with no particular order to the categories. 2. The ordinal level of measurement presumes that one classification is ranked higher than another. 3. The interval level of measurement has the ranking characteristic of the ordinal level of measurement plus the characteristic that the distance between values is a constant size. 4. The ratio level of measurement has all the characteristics of the interval level, plus there is a meaningful zero point and the ratio of two values is meaningful.

frequency table is a grouping of qualitative data into mutually exclusive (distinctive) classes showing the number of observations in each class. The number of observations in each class is called the class frequency. relative class frequencies: to show the fraction of the total number of observations in each class. A relative frequency captures the relationship between a class total and the total number of observations. bar chart: graphically describes a frequency table using a series of uniformly wide rectangles. The horizontal axis shows the classes corresponding to the variable of interest. The vertical axis shows the frequency or relative frequency of each of the possible outcomes. A distinguishing characteristic of a bar chart is that there is a distance or gap between the bars. frequency distribution: is a grouping of quantitative data into mutually exclusive classes showing the number of observations in each class. We construct a frequency distribution by using the following steps: 1. Decide on the number of classes. (“2 to the k rule”) 2. Determine the class width. i is ≥ (max. value – min. value)/k 3. Set the individual class limits. 4. Tally the observations into the classes. 5. Count the number of items in each class. relative frequency distribution: converts each frequency to a relative frequency. To convert a frequency distribution to a relative frequency distribution, each of the class frequencies is divided by the total number of observations. Graphic Presentation of a Frequency Distribution: Histogram: for a frequency distribution based on quantitative data is similar to a bar chart showing the distribution of qualitative data. The classes are marked on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars. (bars touch). Adv: Depicts each class as a rectangle, with the height of the rectangular bar representing the number in each class. frequency polygon: also shows the shape of a distribution and is similar to a histogram. It consists of line segments connecting the points formed by the intersections of the class midpoints and the class frequencies. The midpoint of each class is scaled on the X-axis and the class frequencies on the Y-axis. Adv: Allows us to compare directly two or more frequency distributions by constructing one on top of the other. Median of grouped data: Cumulative Frequency Distribution:

Chapter 3: population mean: is the sum of all the population values divided by the total number of population values. sample mean: is the sum of all the sample values divided by the total number of sampled values. The median: is the midpoint of the values after they have been ordered from the minimum to the maximum. There are as many values above the median as below it in the data array. For an even set of values, the median will be the arithmetic average of the two middle numbers The mode: is the value of the observation that appears most frequently. The weighted mean: is used when there are several observations of the same value.

Standard deviation of grouped data:

The range: is the difference between the largest and the smallest value in a data set.

Range=Maximum value−Minimum value The mean deviation: is the arithmetic mean of the absolute values of the deviations from the arithmetic mean. box plot: is a graphical display, based on quartiles, that helps to picture a set of data

The population variance: is the arithmetic mean of the squared deviations from the population mean.

Chapter 4: A probability: is a measure of the likelihood that an event in the future will happen. An experiment: is a process that leads to the occurrence of one and only one of several po An outcome: is a particular result of an experiment. An event: is a collection of one or more outcomes of an experiment. Classical probability: is based on the assumption that the outcomes of an experiment are equally likely. Possibility of event happening = number of favorable outcomes / number of possible outcomes Events are mutually exclusive: if occurrence of one event means that none of the other events can occur at the same time Events are collectively exhaustive: if at least one of the events must occur when an experiment is conducted. Empirical probability, or relative frequency: is the second type of objective probability. It is based on the number of times an event occurs as a proportion of a known number of trials. Empirical Probability = Number of times the event occurs / total number of observations

m

The Multiplication Formula: If there are there are Arithmetic mean of grouped data:

mxn

ways of doing both.

ways of doing one thing and n ways of doing another thing, Totalnumber of arrangements=( m) ( n )

The Permutation Formula: Any arrangement of r objects selected from a single group of n possible objects when order is considered.

population standard deviation: is the square root of the population variance. Sample Variance: The Combination formula: is the number of ways to choose r objects from a group of n objects without regard to order. ^ The Rules of Addition: If two events A and B are mutually exclusive, the probability of one or the other events occurring equals the sum of their probabilities. Sample standard deviation: the square root of the sample variance Chebyshev’s Theorem: For any set of observations (sample or population), the proportion of the values that lie within k standard deviations of the mean is at least 1-1/k2, where k is any constant greater than 1. Allows us to determine the minimum proportion of the values that lie within a specified number of standard deviations of the mean. The Empirical Rule: For a symmetrical, bell-shaped frequency distribution: 1) Approximately 68 percent of the observations will lie within ±1 standard deviation of the mean. 2) About 95 percent of the observations will lie within ±2 standard deviations of the mean. 3) Practically all (99.7 percent) will lie within ±3 standard deviations of the mean.

P ( A∨B )=P ( A ) + P ( B )

The Complement Rule: Sometimes it is easier to calculate the probability of an event not happening. The complement rule is used to determine the probability of an event occurring by subtracting the probability of the event not occurring from 1.

P ( A )=1−P ( A) Joint Probability: A probability that measures the likelihood two or more events will happen concurrently is called a joint probability. Pictured below is the joint probability of A and B, P(A and B). The General Rule of Addition: If A and B are two events that are not mutually exclusive(they can happen at the same time), then P(A or B) is given by the following formula:

P ( A∨B )=P ( A ) + P ( B )−P ( A∧B )

The Rules of Multiplication: The special rule of multiplication requires that two events, A and B, be independent. Two events are independent if the occurrence of one does not alter the probability of the occurrence of the other event.

P ( A∧B )=P ( A ) P ( B )...