55. A small company records the number of online orders it receives each day for a week (Monday to Sunday). The numbers of orders are as ps: follows: 10, 12, 15, 8, 20, 15, and 18. What is the standard deviation of the number of orders? A. 5.87 B. 4.67 C. 4.28 D. 1.36
Question
- A small company records the number of online orders it receives each day for a week (Monday to Sunday). The numbers of orders are as ps: follows: 10, 12, 15, 8, 20, 15, and 18. What is the standard deviation of the number of orders? A. 5.87 B. 4.67 C. 4.28 D. 1.36
Solution 1
To calculate the standard deviation, follow these steps:
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Find the mean (average) of the numbers. Add all the numbers together and divide by the total number of numbers. In this case, (10+12+15+8+20+15+18)/7 = 98/7 = 14.
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Subtract the mean from each number to get the deviation of each number. This would be -4, -2, 1, -6, 6, 1, 4.
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Square each deviation. This would be 16, 4, 1, 36, 36, 1, 16.
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Find the mean of these squared deviations. This would be (16+4+1+36+36+1+16)/7 = 110/7 = 15.71.
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Take the square root of this mean squared deviation. The square root of 15.71 is approximately 3.96.
So, the standard deviation of the number of orders is approximately 3.96. However, this option is not available in the choices. It seems there might be a mistake in the problem or the answer choices.
Solution 2
To calculate the standard deviation, follow these steps:
-
Find the mean (average) of the numbers. Add all the numbers together and divide by the total number of numbers. In this case, (10+12+15+8+20+15+18)/7 = 98/7 = 14.
-
Subtract the mean from each number to get the deviation of each number. This gives you: -4, -2, 1, -6, 6, 1, 4.
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Square each deviation to get: 16, 4, 1, 36, 36, 1, 16.
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Find the mean of these squared deviations. Add them all together and divide by the total number. (16+4+1+36+36+1+16)/7 = 110/7 = 15.71.
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The standard deviation is the square root of this mean squared deviation. The square root of 15.71 is approximately 3.96.
So, the standard deviation of the number of orders is not listed in the options A, B, C, or D. There might be a mistake in the question or the provided options.
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