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Flashcards: Statistics 20 Flashcards 
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Card: 1 / 20 
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What is the definition of the mean in a data set? |
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Card: 2 / 20
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The mean, often referred to as the average, is calculated by adding all the values in a data set and then dividing by the number of values. For example, for the data set {2, 3, 5}, the mean is (2 + 3 + 5) / 3 = 10 / 3 ≈ 3.33. |
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Card: 3 / 20
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What is the difference between the mean and the median? |
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Card: 4 / 20
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The mean is the average of all data points, while the median is the middle value when the data points are arranged in ascending order. If there is an even number of values, the median is the average of the two middle numbers. For example, in the data set {1, 3, 3, 6, 7, 8}, the median is (3 + 6) / 2 = 4.5. |
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Card: 5 / 20
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How is standard deviation calculated, and what does it signify? |
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Card: 6 / 20
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Standard deviation measures the amount of variation or dispersion in a set of values. It is calculated by taking the square root of the variance. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range. |
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Card: 7 / 20
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If a data set has a mean of 50 and a standard deviation of 5, what percentage of the data falls within one standard deviation of the mean? |
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Card: 8 / 20
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According to the Empirical Rule, approximately 68% of the data in a normal distribution falls within one standard deviation of the mean. Therefore, for a mean of 50 and a standard deviation of 5, about 68% of the data lies between 45 and 55. |
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Card: 9 / 20
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What is a correlation coefficient, and what does a value of -0.8 indicate? |
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Card: 10 / 20
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The correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. A value of -0.8 indicates a strong negative correlation, meaning that as one variable increases, the other variable tends to decrease. |
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Card: 11 / 20
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What is the formula for variance in a data set? |
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Card: 12 / 20
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Variance is calculated as the average of the squared differences from the mean. The formula is: Variance = Σ(x - mean)² / N, where x represents each data point and N is the number of data points. |
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Card: 13 / 20
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How do you interpret a box plot? |
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Card: 14 / 20
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A box plot visually summarizes the distribution of a data set. It shows the median, quartiles, and potential outliers. The box represents the interquartile range (IQR), with a line indicating the median, while the 'whiskers' extend to the smallest and largest values within 1.5 times the IQR from the quartiles. |
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Card: 15 / 20
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What is the purpose of a z-score? |
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Card: 16 / 20
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A z-score indicates how many standard deviations an element is from the mean. It is calculated as z = (x - mean) / standard deviation. Z-scores are useful for comparing scores from different distributions. |
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Card: 17 / 20
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In a normal distribution, what percentage of data falls within two standard deviations of the mean? |
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Card: 18 / 20
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In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean, according to the Empirical Rule. |
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Card: 19 / 20
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If the mode of a data set is 4, what does that indicate? |
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Card: 20 / 20
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The mode is the value that appears most frequently in a data set. If the mode is 4, it means that 4 occurs more often than any other number in the data set. |
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 Completed! Keep practicing to master all of them. |
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