Question

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

Answer 1

It is periodic with period of 3 and amplitude of about 7.5.

Answer 2

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