Cheet Sheet for Amdm Unit 4
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A Cheat Sheet for Amdm Unit 4: Statistics
Unit 4 of Advanced Mathematical Decision Making (AMDM) focuses on statistics, the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. This unit covers a variety of topics, including the measures of central tendency, measures of variability, and probability. In this cheat sheet, we will provide you with a summary of the key concepts and formulas covered in Unit 4 to help you prepare for your AMDM exams.
Measures of Central Tendency
Measures of central tendency are statistics that summarize the center of a data set. The three most common measures of central tendency are the mean, median, and mode.
1. Mean: The mean is the average of a set of numbers. To calculate the mean, add up all the numbers in the data set and then divide the sum by the number of values in the set.
Mean = (Sum of all values) / (Number of values)
2. Median: The median is the middle value in a data set when the values are arranged in numerical order. If there is an even number of values, the median is the average of the two middle values.
3. Mode: The mode is the value that appears most frequently in a data set.
Measures of Variability
Measures of variability describe the spread or dispersion of a data set. The three most common measures of variability are the range, variance, and standard deviation.
1. Range: The range is the difference between the largest and smallest values in a data set.
Range = Largest value – Smallest value
2. Variance: The variance measures how spread out the values in a data set are from the mean. To calculate the variance, subtract the mean from each value, square the result, sum up all the squared differences, and then divide by the number of values.
Variance = Σ (xᵢ – μ)² / n
3. Standard Deviation: The standard deviation is the square root of the variance. It gives an indication of how spread out the values in a data set are from the mean.
Probability
Probability is the likelihood of an event occurring. In Unit 4, you will learn about the different types of probability, including theoretical probability, experimental probability, and conditional probability.
1. Theoretical Probability: Theoretical probability is the likelihood of an event occurring based on the total number of possible outcomes. It is calculated by dividing the number of favorable outcomes by the total number of outcomes.
Theoretical Probability = (Number of favorable outcomes) / (Total number of outcomes)
2. Experimental Probability: Experimental probability is the likelihood of an event occurring based on the results of an experiment or observation. It is calculated by dividing the number of times the event occurs by the total number of trials.
Experimental Probability = (Number of times event occurs) / (Total number of trials)
3. Conditional Probability: Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is calculated by dividing the probability of both events occurring by the probability of the given event occurring.
Conditional Probability = P(A and B) / P(A)
Bayes’ Theorem
Bayes’ Theorem is a formula used to find the probability of an event based on prior knowledge. It is commonly used in statistics and probability to update the probability of an event as new information becomes available.
Bayes’ Theorem: P(A|B) = [P(B|A) * P(A)] / P(B)
Where:
– P(A|B) is the probability of event A given that event B has occurred.
– P(B|A) is the probability of event B given that event A has occurred.
– P(A) is the probability of event A.
– P(B) is the probability of event B.
Hypothesis Testing
Hypothesis testing is a statistical technique used to make inferences about a population based on sample data. In Unit 4, you will learn about hypothesis testing, including null and alternative hypotheses, test statistics, p-values, and significance levels.
1. Null Hypothesis (H₀): The null hypothesis is the default assumption that there is no significant difference or effect.
2. Alternative Hypothesis (H₁): The alternative hypothesis is the assertion that there is a significant difference or effect.
3. Test Statistic: The test statistic is a numerical value used to make a decision about the null hypothesis. It is calculated using sample data and the null hypothesis.
4. P-value: The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming that the null hypothesis is true. A smaller p-value indicates stronger evidence against the null hypothesis.
5. Significance Level: The significance level is the threshold at which the null hypothesis is rejected. It is typically set at α = 0.05.
Conclusion
Unit 4 of AMDM covers a wide range of statistical concepts, including measures of central tendency, variability, probability, hypothesis testing, and Bayes’ Theorem. By familiarizing yourself with the key concepts and formulas presented in this cheat sheet, you will be better prepared to tackle the statistical problems that you encounter in your AMDM exams. Good luck with your studies, and remember to practice, practice, practice!
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