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daser333 [38]
2 years ago
8

Consider a nine -year moving average used to smooth a time series that was first recorded in 1961. a. Which year serves as the f

irst centered value in the smoothed series? b. How many years of values in the series are lost when computing all the nine-year moving averages?
Mathematics
1 answer:
kirill [66]2 years ago
5 0

Answer:

  a.  1965

  b.  8 years

Step-by-step explanation:

For answers to questions like these it can work to consider the smallest possible dataset.

<h3>Dataset</h3>

For our purpose, consider the 9 years/values to be averaged to be ...

  1, 2, 3, 4, 5, 6, 7, 8 ,9

<h3>Observations</h3>

a. The center value of the data set is 5. Its number is 5-1=4 more than the first one.

The first centered value is from the year 1961 +4 = 1965.

b. The 4 values at the beginning, and the 4 values at the end do not have a corresponding "average" value. That is, 4+4 = 8 values in the series are lost with respect to the number of average values.

8 years of values are lost.

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Answer:

Stefan spend $120 originally.

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Step-by-step explanation:

Given:

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Solution:

Let the Amount Stefan spend originally be 'x'.

Total Cost of Jim is equal to sum of Cost of bicycle and Cost of Helmet.

framing in equation form we get;

Total Cost of Jim = 175+17 =\$192

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framing in equation form we get;

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Dividing both side by 1.6 we get;

\frac{192}{1.6}=\frac{1.6x}{1.6}\\\\x= \$120

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Now we can say that;

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framing in equation form we get;

Money Stefan made = 192-120 =\$72

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Answer:

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Step-by-step explanation:

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