Chapter 1. Measuring Spread: the Standard Deviation

Correct. Both histograms are centered at the same place.

Incorrect. Both histograms are centered at the same place.

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Correct. The histogram for Atlanta temperatures is much wider than the histogram for San Diego temperatures.

Incorrect. The histogram for Atlanta temperatures is much wider than the histogram for San Diego temperatures.

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Correct. The histograms are both centered at the same place.

Incorrect. The histograms are both centered at the same place.

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Correct. The histogram for SWBDX percent return is narrower than the histogram for SWLBX percent return.

Incorrect. The histogram for SWBDX percent return is narrower than the histogram for SWLBX percent return.

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Correct. A deviation is equivalent to the distance a value is from the mean. So, a deviation is the difference between the observation value and the mean, \( \overline{x} \).

Incorrect. A deviation is equivalent to the distance a value is from the mean. So, a deviation is the difference between the observation value and the mean, \( \overline{x} \).

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Correct. Since the observations below the mean have negative deviations and the observations above the mean have positive deviations and the mean is the balance point, the sum of these deviations is always zero.

Incorrect. Since the observations below the mean have negative deviations and the observations above the mean have positive deviations and the mean is the balance point, the sum of these deviations is always zero.

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Correct. “s” is the symbol for sample standard deviation.

Incorrect. “s” is the symbol for sample standard deviation.

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Correct. Variance is the average of the squared deviations. Since a squared deviation is graphically represented by an area, variance is the area of the average squared deviation.

Incorrect.Variance is the average of the squared deviations. Since a squared deviation is graphically represented by an area, variance is the area of the average squared deviation.

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Correct. It would be nice to either delete the negative signs or to take absolute values, but mathematically, this is too messy. Using squared the deviations has nice mathematical properties.

Incorrect. It would be nice to either delete the negative signs or to take absolute values, but mathematically, this is too messy. Using squared the deviations has nice mathematical properties.

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Correct. This is a correct statement.

Incorrect. This is a correct statement.

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Correct. Since variance is the average of the squared deviations and we find standard deviation by taking its square root, standard deviation is the length of one side of the average squared deviation.

Incorrect. Since variance is the average of the squared deviations and we find standard deviation by taking its square root, standard deviation is the length of one side of the average squared deviation.

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Correct. No one likes to spend time computing standard deviation by hand.

Incorrect. No one likes to spend time computing standard deviation by hand.

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Correct. We always take the positive square root of variance when we compute standard deviation. Standard deviation is zero when all of the observations have the same value.

Incorrect. We always take the positive square root of variance when we compute standard deviation. Standard deviation is zero when all of the observations have the same value.

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Correct. Standard deviation measures variability. This is very important to know.

Incorrect. Standard deviation measures variability. This is very important to know.

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Correct. When all of the values in a data set are the same, their standard deviation is zero.

Incorrect. When all of the values in a data set are the same, their standard deviation is zero.

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Correct. ‘26’ is an outlier and will inflate standard deviation as it adds more variability. The more the data vary from the mean, the greater the standard deviation.

Incorrect. ‘26’ is an outlier and will inflate standard deviation as it adds more variability. The more the data vary from the mean, the greater the standard deviation.

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Correct. Standard deviation has the same unit of measure as the data.

Incorrect. Standard deviation has the same unit of measure as the data.

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Correct. We divide by “n – 1” when computing sample standard deviation for mathematical reasons.

Incorrect. We divide by “n – 1” when computing sample standard deviation for mathematical reasons.

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Correct. Since outliers affect the mean and the mean is used in computing standard deviation, standard deviation is also affected by outliers. In fact, an outlier always increases standard deviation.

Incorrect. Since outliers affect the mean and the mean is used in computing standard deviation, standard deviation is also affected by outliers. In fact, an outlier always increases standard deviation.

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Correct. range = maximum minus minimum = 47 – 34 = 13

Incorrect. range = maximum minus minimum = 47 – 34 = 13

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Correct. Range = maximum minus minimum = 540 – 360 = 180 and 180/6 = 30. Note that 360 and 540 are approximations.

Incorrect. Range = maximum minus minimum = 540 – 360 = 180 and 180/6 = 30. Note that 360 and 540 are approximations.

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Correct. Range = 5125 – 1625 = 3500 and 3500/6 = 583.33 or approximately 600 grams.

Incorrect. Range = 5125 – 1625 = 3500 and 3500/6 = 583.33 or approximately 600 grams.

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Correct. Outliers always inflate standard deviation so the standard deviation computed with these seven extreme values will be greater than the standard deviation computed without these seven extreme values.

Incorrect. Outliers always inflate standard deviation so the standard deviation computed with these seven extreme values will be greater than the standard deviation computed without these seven extreme values.

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Correct. Since the temperatures in San Diego are less variable than the temperatures in Atlanta, San Diego will give a more stable climate.

Incorrect. Since the temperatures in San Diego are less variable than the temperatures in Atlanta, San Diego will give a more stable climate.

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Correct. The Schwab total market bond index has more variability and consequently, has a possibility of giving a greater return. It also has the possibility of giving a lower return.

Incorrect. The Schwab total market bond index has more variability and consequently, has a possibility of giving a greater return. It also has the possibility of giving a lower return.

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