Ch 3 Warm-up

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Feb 20, 2024

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Ch 3: Warm up 1. In your own words, explain what the standard deviation is. Standard deviation is a measure that is related on how the data values are away from the mean on average 2. Here are three distributions. The distributions have the same scale and the same number of data points, so they are easy to compare. The three distributions (A, B and C) all have a mean of 5. Which distribution has the smallest standard deviation? Justify your answer. NOTE: You don’t have to calculate anything. a. Which distribution has the smallest standard deviation? Justify your answer. NOTE: You don’t have to calculate anything. The distribution number C because has the list of the smallest data away from the mean. b. Which distribution has the largest standard deviation? Justify your answer. The distribution number A has the largest standard deviation because the distribution has all of the data values away from the mean. 3. These two distributions have the same scale. In both distributions, the mean is at 10 and we see that all of the data stacked at the mean except for two data points at 9 and one at 12. The sample on the left is larger (8 data points vs. 6 data points.) Which distribution has the smallest standard deviation? Why? Explain?

Distribution A has the smallest deviation because it has more data points than B and it makes the standard deviation smallest. 4. In your own words, explain what a z-score is. The number of standard deviations that a value is above or below the mean. 5. Based on sample data, newborn males have weights with a mean of 3296.3 g and a standard deviation of 885.7 g. Newborn females have weights with a mean of 3018.2 g and a standard deviation of 522.4 g. Identify who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g? Why? Explain. Round to two decimal places. For males is -1.80 For females is -2.52 Relative to their gender a newborn female who weights 1700g would be more extreme or significantly low since 1700g is more than two standard deviations below the mean. 6. If Albert’s score on the Midterm exam was 78 out of 100 and this score fell in the 75 th percentile, what does this mean? Explain. This means that 75 percent of the total grades were less than or equal to 78, and 25 percent were greater than 78. This means that 75% of Albert’s class scored 78% or below on the midterm score.

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