Statistical Studies, Vocabulary, Empirical Rule, and Z-Score

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What is a z-score?

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A z-score indicates how many standard deviations an element is from the mean. It is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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How do you calculate a z-score?

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To calculate a z-score, use the formula: z = (X - μ) / σ. For example, if a student scored 88, the class average is 76, and the standard deviation is 7.5, the z-score is (88 - 76) / 7.5 = 1.6.

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What type of study involves randomly assigning subjects to different groups to test a hypothesis?

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An experiment.

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What is an observational study?

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An observational study is a type of research where the researcher observes subjects without manipulating any variables. It is used to identify correlations.

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What is a survey in research?

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A survey is a method of collecting data by asking questions to a group of people to gather information about their opinions, behaviors, or characteristics.

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What does it mean if data is skewed right?

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If data is skewed right, it means that the tail on the right side of the distribution is longer or fatter than the left side, indicating that there are a number of high values.

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What is the empirical rule in statistics?

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The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.

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What is the difference between an experiment and a survey?

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An experiment involves manipulating variables to determine cause-and-effect relationships, while a survey collects data without manipulation to understand opinions or behaviors.

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What is a random sample?

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A random sample is a subset of individuals chosen from a larger set, where each individual has an equal chance of being selected, ensuring that the sample represents the population.

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What is the purpose of using a control group in an experiment?

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A control group is used to provide a baseline for comparison, helping to isolate the effect of the independent variable being tested.