Question

Is the data set approximately periodic? If so, what are it's period and amplitude?

Day| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
Books Borrowed 102 | 76 | 91 | 140 | 98 | 74 | 88 | 137 | 100 | 75 | 92 | 139
• not periodic
• periodic with a period of 4 and an amplitude of about 20
• periodic with a period of 4 and an amplitude of about 30
• periodic with a period of 5 and an amplitude of about 25

Answer 1

First of all, look for the peak value after which the value again starts to decrease.
Interpolating from the table, as we can see peak values have a 4 day gap.

So the period is 4 days

Here, the peak value = sum of all peak / number of peaks = 129.5
Here the mean values = are sum of all value/ total days =101

Hence, amplitude = 2(peak-mean) = (129.5-101) = 19.5 = 20

Therefore, the correct answer is B) periodic with a period of 4 and amplitude of about 20