Is the data set approximately periodic? If so, what are its period and amplitude?

Question

asked Dec 18, 2018 20.2k views

2 Answers

Pkaeding · Answer 1 · 2018-12-21T20:56:09+0000

Answer:

The correct option is:

Periodic with period 3 and amplitude of about 7.5

Explanation:

We are given a data set as:

Hour Number of bikes

1 5

2 19

3 14

4 4

5 19

6 15

7 6

8 22

9 15

10 5

11 20

12 16

From this data set we could clearly observe that the values are periodic as it repeats after every 3rd value.

{(1,5), (2,19) , (3,14)} {(4,4),(5,19),(6,15)} {(7,6),(8,22),(9,15)} {(10,5),(11,20),(12,16)}

Also, the amplitude is the distance is calculated as:

$(Largest\ value-Smallest\ value)/(2)$

( Since, amplitude is the distance of the maximum or minimum value from the mid-line)

for first set:

$Amplitude=(19-5)/(2)\\\\Amplitude=7$

for second set:

$Amplitude=(19-4)/(2)\\\\Amplitude=7.5$

for third set:

$Amplitude=(22-6)/(2)\\\\Amplitude=8$

for fourth set:

$Amplitude=(20-5)/(2)\\\\Amplitude=7.5$

Hence, approximately the amplitude is:

7.5