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Answer :
The measurements (60, 63, and 61.5 inches) are biased as they are all higher than the true height of 59 inches. The variance of these measurements is calculated to be 1.5.
Given your true height is 59 inches, and your measurements are 60 inches, 63 inches, and 61.5 inches, we first need to determine if these measurements are biased. In this case, all measurements are greater than 59 inches, indicating a potential upward bias.
Now let's calculate the variance of these measurements:
- Find the mean (average) of the measurements:
Mean = (60 + 63 + 61.5) / 3 = 61.5 inches. - Calculate the squared differences from the mean:
(60 - 61.5)² = 2.25, (63 - 61.5)² = 2.25, (61.5 - 61.5)² = 0. - Average these squared differences (variance):
Variance = (2.25 + 2.25 + 0) / 3 = 1.5.
Therefore, the variance of your measurements is 1.5.
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Final answer:
The measurements are biased since they consistently exceed the actual height of 59 inches. The variance of these measurements, indicating their spread or dispersion, is 1.5 inches squared.
Explanation:
If a measurement is biased, it means that it persistently deviates from the true value. In this case, your actual height is 59 inches, and the measurements you obtained were 60 inches, 63 inches, and 61.5 inches. Therefore, these measurements can be considered biased since they consistently exceed your actual height.
The variance of these measurements can be determined using the following steps:
- Find the mean (average) of these measurements: (60 + 63 + 61.5) ÷ 3 = 61.5 inches
- Deduct the mean from each measurement and square the results: (60 - 61.5)^2 = 2.25, (63 - 61.5)^2 = 2.25, and (61.5 - 61.5)^2 = 0
- Find the mean of these squared differences: (2.25 + 2.25 + 0) ÷ 3 = 1.5. So, the variance of your height measurements is 1.5 inches squared.
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