Standard Deviation quiz #3 Flashcards
Standard Deviation quiz #3
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Which weights are within 2 standard deviations of the mean? Weights within the interval [mean - 2s, mean + 2s] are within 2 standard deviations of the mean. Which statement is true about standard deviation? Standard deviation uses all data values and is sensitive to outliers. If the sample variance of hourly wages is 10, what is the sample standard deviation? Sample standard deviation is sqrt(10). What effect does removing an outlier have on the standard deviation? Removing an outlier typically decreases the standard deviation. Of what is standard deviation a direct measure? Standard deviation directly measures the spread or variability of data values. How do you calculate the variance of a data set such as 0.0625, 0.25, 0.5, 1.5? Find the mean, subtract it from each value, square the differences, sum them, and divide by (n-1). Why is the range less desirable than the standard deviation as a measure of dispersion? Range only considers the extremes, while standard deviation uses all data values. What can be said about a set of data with a standard deviation of 0? All values are identical; there is no spread. What happens to the graph of the normal curve as the mean increases? The curve shifts to the right, but its shape remains unchanged. Which is not a property of the standard deviation? Standard deviation cannot be negative. How can you tell which histogram depicts a higher standard deviation? The histogram with more spread out data has a higher standard deviation. Why is the standard deviation used more frequently than the variance? Standard deviation is in the same units as the data, making it easier to interpret. If the standard deviation for a set of data is 0, what does this indicate? All data values are identical; there is no spread. Given the mean of a normal distribution, what does the standard deviation indicate? Standard deviation indicates how spread out the values are around the mean. What proportion of data is within one standard deviation of the mean in a normal distribution? Approximately 68% of data is within one standard deviation of the mean. Which group of scores would have the smallest standard deviation? The group with values closest to each other (least spread) has the smallest standard deviation. Why is the standard deviation preferable to the range as a measure of variation? Standard deviation uses all data values and reflects overall variability, while range only uses extremes. Which characteristic does not describe a normal distribution? A normal distribution is not skewed; it is symmetric. How can the standard deviation be used to specify uncertainty? Standard deviation quantifies the typical deviation from the mean, indicating uncertainty in measurements. When is an observation considered an outlier? An observation is considered an outlier if it is more than 2 or 3 standard deviations from the mean. What is the range rule of thumb for estimating the standard deviation? Standard deviation ≈ range / 4. What does the z-score represent in statistics? The z-score represents the number of standard deviations an observation is from the mean. For a bell-shaped data set, approximately what proportion of data falls within two standard deviations of the mean? Approximately 95% of data falls within two standard deviations of the mean. What is the range rule of thumb for estimating the standard deviation of a data set? Standard deviation ≈ range / 4. What can be said about a set of data with a standard deviation of 0? All values are identical; there is no spread. What happens to the graph of the normal curve as the mean increases? The curve shifts to the right, but its shape remains unchanged. Which is not a property of the standard deviation? Standard deviation cannot be negative. How can you tell which histogram depicts a higher standard deviation? The histogram with more spread out data has a higher standard deviation. Why is the standard deviation used more frequently than the variance? Standard deviation is in the same units as the data, making it easier to interpret. If the standard deviation for a set of data is 0, what does this indicate? All data values are identical; there is no spread. Which characteristic of data measures the amount that the data values vary? Standard deviation measures the amount that data values vary. What must be known about a data set before the empirical rule can be used? The data set must be approximately normally distributed. Why is the standard deviation preferable to the range as a measure of variation? Standard deviation uses all data values and reflects overall variability. Is standard deviation a resistant measure of spread? No, standard deviation is not resistant; it is sensitive to outliers. What describes the usefulness of a standard deviation? Standard deviation quantifies variability and helps compare the spread of different data sets. Which set of data will have the smallest standard deviation? The set with values closest to each other (least spread) will have the smallest standard deviation. Approximately what percent of people score lower than three standard deviations below the mean? Approximately 0.15% of people score lower than three standard deviations below the mean in a normal distribution. Which symbol identifies the sample standard deviation? The symbol s identifies the sample standard deviation. What can be said about a set of data with a standard deviation of 0? All values are identical; there is no spread. Which is not a property of the standard deviation? Standard deviation cannot be negative.
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