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Answer :
To determine if the data set is periodic, we need to see if there is a repeating pattern in the values. We also have to find out the period and amplitude of this pattern if it exists.
Data Set:
```
Days: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Cars washed: 36, 21, 44, 15, 30, 8, 9, 29, 16, 45, 20, 34
```
Step 1: Check for Periodicity with a Period of 6
1. Split the data into two segments, each with 6 data points:
- Segment 1: Days 1 to 6 → [36, 21, 44, 15, 30, 8]
- Segment 2: Days 7 to 12 → [9, 29, 16, 45, 20, 34]
2. Compare these two segments to see if they show a similar pattern. To do this, we can look at their average values and see if they're close. Calculate the average (mean) of each segment:
- Mean of Segment 1: (36 + 21 + 44 + 15 + 30 + 8) / 6 = 154 / 6 ≈ 25.67
- Mean of Segment 2: (9 + 29 + 16 + 45 + 20 + 34) / 6 = 153 / 6 ≈ 25.5
3. Calculate the amplitude, which is half the difference between the maximum and minimum values of both segments combined:
- Max value: 45
- Min value: 8
- Amplitude: (45 - 8) / 2 = 37 / 2 = 18.5
4. Assess if the data is periodic by comparing the two segment means. If they are close enough, it suggests periodicity with the suggested period (here, that's within the range given by half the amplitude).
Conclusion:
The data set exhibits a pattern with a period of 6 days and an amplitude of approximately 18.5, showing it is approximately periodic.
Data Set:
```
Days: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
Cars washed: 36, 21, 44, 15, 30, 8, 9, 29, 16, 45, 20, 34
```
Step 1: Check for Periodicity with a Period of 6
1. Split the data into two segments, each with 6 data points:
- Segment 1: Days 1 to 6 → [36, 21, 44, 15, 30, 8]
- Segment 2: Days 7 to 12 → [9, 29, 16, 45, 20, 34]
2. Compare these two segments to see if they show a similar pattern. To do this, we can look at their average values and see if they're close. Calculate the average (mean) of each segment:
- Mean of Segment 1: (36 + 21 + 44 + 15 + 30 + 8) / 6 = 154 / 6 ≈ 25.67
- Mean of Segment 2: (9 + 29 + 16 + 45 + 20 + 34) / 6 = 153 / 6 ≈ 25.5
3. Calculate the amplitude, which is half the difference between the maximum and minimum values of both segments combined:
- Max value: 45
- Min value: 8
- Amplitude: (45 - 8) / 2 = 37 / 2 = 18.5
4. Assess if the data is periodic by comparing the two segment means. If they are close enough, it suggests periodicity with the suggested period (here, that's within the range given by half the amplitude).
Conclusion:
The data set exhibits a pattern with a period of 6 days and an amplitude of approximately 18.5, showing it is approximately periodic.
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