INTERQUARTILE RANGE OF INTRA-DAY MERITS WITH TIME SERIES PLOT
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In short, again, interquartile range represents for 50% of observed data points.
For instance, if you have 100 data points (100 days over weeks), the interquartile range will represents for 50 datapoints in the 'middle range', that ranges from the 25th quartile to the 75th quartile. Interquartile range has its role to exclude outliers, such as maximum, minimum and some extreme large and small data points closely with max and min.
In the same way, median represents nearly the true mean (average) of observed data. It is better than what we usually use, mean or average.
Both median and interquartile range exclude effects from outliers.
Time series plot of median and interquartile rangeNotes:
- p25 ~q1;
- p75 ~ q3.
The interquartile range (IQR) ranges from p25 (q1) to p75 (q3), and the IQR represents 50% of observed days.
For example, with the week #2019w13, 50% of of days observed till the end of #2019w13 have their total intra-day merits change from 522 (p25 ~ q1) to 764 (p75 ~ q3).
The median of the same period is 626, it means that there are 50% of observed days have intra-day merits below 626, while the rest 50% of observed days have intra-day merits above 626.
. list week merit median q1 q3
+------------------------------------------+
| week merit median q1 q3 |
|------------------------------------------|
39. | 2019w13 6120 626 522 764 |
Dataset for median, interquartile range of intraday merits. list week merit median q1 q3
+------------------------------------------+
| week merit median q1 q3 |
|------------------------------------------|
1. | 2018w26 4457 733 609 991 |
2. | 2018w27 4253 715 598 979 |
3. | 2018w28 4239 707 592 963 |
4. | 2018w29 4159 693 589 922 |
5. | 2018w30 3652 684 577 902 |
|------------------------------------------|
6. | 2018w31 3798 682 575 891 |
7. | 2018w32 3994 675 567 880 |
8. | 2018w33 3618 667 559 867 |
9. | 2018w34 3789 652 555 848 |
10. | 2018w35 3065 642 537 844 |
|------------------------------------------|
11. | 2018w36 3574 639 528 838 |
12. | 2018w37 5630 634 528 829 |
13. | 2018w38 7825 641 530 846 |
14. | 2018w39 4388 640 531 839 |
15. | 2018w40 4271 639 528 829 |
|------------------------------------------|
16. | 2018w41 3800 637 528 808 |
17. | 2018w42 4821 639 530 807 |
18. | 2018w43 3945 639 528 801 |
19. | 2018w44 3339 628 521 796 |
20. | 2018w45 4513 630 522 789 |
|------------------------------------------|
21. | 2018w46 3722 626 521 786 |
22. | 2018w48 3750 626 521 774 |
23. | 2018w49 3560 621.5 517 773 |
24. | 2018w50 3782 619 517 768 |
25. | 2018w51 3753 618.5 515 766.5 |
|------------------------------------------|
26. | 2018w52 3278 616.5 509.5 762.5 |
27. | 2019w1 4793 616 510 766 |
28. | 2019w2 6624 618.5 513 773 |
29. | 2019w3 5306 620 514 774 |
30. | 2019w4 4659 621.5 516.5 770.5 |
|------------------------------------------|
31. | 2019w5 4474 620 516 773 |
32. | 2019w6 4318 619.5 517 768 |
33. | 2019w7 4207 618 519 767 |
34. | 2019w8 4507 618.5 518.5 766.5 |
35. | 2019w9 4625 619 518 766 |
|------------------------------------------|
36. | 2019w10 4901 623 521 764 |
37. | 2019w11 4318 623 521 761 |
38. | 2019w12 4598 625.5 521 759.5 |
39. | 2019w13 6120 626 522 764 |
Data source:- From LoyceV's weekly data dumps.
- From my converted datasets in the topic:
Time Series Analysis on Distributed Merits in the forum (daily, weekly, monthly)