This investigation aims at identifying numerical pattern(s) of number of verses (ayas) in different chapters (suras) of the Quran using statistical analysis. It includes the mean, mode [1], median [2], range [3], standard deviation (SD) [4], and relative standard deviation (RSD) [5]. The study uses three different methods of grouping Qur'anic chapters.

 

The tables and figures in this study also provide useful information about the structure of the Qur'an.

 

I. Introduction
Briefly, the Quran was revealed in Arabic to the Prophet Mohammad in 610 CE over 22 years. In the first twelve years of the revelation, the Prophet was living in Mecca. Persecution then forced him to leave to Al-Madina, in what is known as the Hijra (immigration), where he lived the last ten years.

 

The 114 chapters of the Holy Quran are not listed in the chronological order of their revelation. This special order, however, was inspired to the Prophet by Allah, so it is a genuine quality of the Qur'an [6]. Each chapter is described as either Meccan or Madinite, depending on whether the majority of its verses were revealed before or after the Hijra.

 

In this work, I will use three different schemes to group the Qur'anic chapters:

 

1. The widely used dual grouping of chapters into Meccan and Madinite.

 

2. The sequential grouping scheme, where each group is formed of consecutive chapters that are all either Meccan or Madinite. For instance, the first chapter in the Qur'an which was revealed in Mecca is followed by four Madinite chapters, which are followed by two Meccan chapters, and so on. Thus chapter 1 is the only member of group 1 (Meccan), chapters 2-5 constitute group 2 (Madinite), chapters 6-7 constitute group 3 (Meccan), and so on. This scheme yields 25 groups.

 

3. The grouping scheme suggested by Mustansir Mir in his article Is The Qur'an A Shapeless Book?, Renaissance, August 1999.

 

I have provided all the primary data in tabular form for those interested in further investigating this topic.

 

II. The Dual Grouping Scheme
Table (1a) gives for each chapter its position or serial number in the Qur'an, the number of verses it has, and its group according to its place of revelation, where M stands for Meccan and H (from Hijra ) for Madinite.

 

Table (1a). The Dual Grouping Scheme

Number	Verses	Type	Number	Verses	Type	Number	Verses	Type
1	7	M	39	75	M	77	50	M
2	286	H	40	85	M	78	40	M
3	200	H	41	54	M	79	46	M
4	176	H	42	53	M	80	42	M
5	120	H	43	89	M	81	29	M
6	165	M	44	59	M	82	19	M
7	206	M	45	37	M	83	36	M
8	75	H	46	35	M	84	25	M
9	129	H	47	38	H	85	22	M
10	109	M	48	29	H	86	17	M
11	123	M	49	18	H	87	19	M
12	111	M	50	45	M	88	26	M
13	43	H	51	60	M	89	30	M
14	52	M	52	49	M	90	20	M
15	99	M	53	62	M	91	15	M
16	128	M	54	55	M	92	21	M
17	111	M	55	78	H	93	11	M
18	110	M	56	96	M	94	8	M
19	98	M	57	29	H	95	8	M
20	135	M	58	22	H	96	19	M
21	112	M	59	24	H	97	5	M
22	78	H	60	13	H	98	8	H
23	118	M	61	14	H	99	8	H
24	64	H	62	11	H	100	11	M
25	77	M	63	11	H	101	11	M
26	227	M	64	18	H	102	8	M
27	93	M	65	12	H	103	3	M
28	88	M	66	12	H	104	9	M
29	69	M	67	30	M	105	5	M
30	60	M	68	52	M	106	4	M
31	34	M	69	52	M	107	7	M
32	30	M	70	44	M	108	3	M
33	73	H	71	28	M	109	6	M
34	54	M	72	28	M	110	3	H
35	45	M	73	20	M	111	5	M
36	83	M	74	56	M	112	4	M
37	182	M	75	40	M	113	5	M
38	88	M	76	31	H	114	6	M

 

I should note that there is disagreement among scholars about whether some chapters were revealed before or after the Hijra. However, the table above reflects the commonly accepted view.

 

The table above also neglects the fact that some scholars think that a number of verses in Meccan chapter were revealed after the Hijra, and a few verses in Madinite chapters were revealed before the Hijra. However, these numbers are too small to have any significant effect on the results of this study.

 

As seen from the table, the total number of chapters is 114 [7], with 86 [8] Meccan and 28 [9] Madinite. Different chapters have different numbers of verses.

 

Exactly 50% of the Meccan chapters, i.e. 43 chapters, have odd serial numbers, and the other half have even serial numbers. Also exactly 50% (i.e. 43) of the Meccan chapters have odd numbers of verses, and the other half have even numbers of verses.

 

Similarly, 50% of the Madinite chapters, that is 14 chapters, have odd serial numbers, and the other half have even serial numbers. Unlike the Meccan chapters, 39.3% of the Madinite chapters, i.e. 11 of them, have odd numbers of verses, and the remaining 60.7 %, i.e. 17, have even numbers of verses.

 

For the whole Qur'an, the number of chapters with odd numbers of verses is 54 (47.4 %) and with even number of verses is 60 (52.6 %).

 

The results of the dual grouping method are summarized in Table (2).

 

Table (2). Results of the dual grouping method

Chapters	Number of chapters	Percentage	Number of verses	Percentage
Meccan	86	75.44	4613	73.97%
Madinite	28	24.56%	1623	26.03%
Total	114	100%	6236	100%

 

Table (3) gives more statistics about the Qur'anic chapters. It shows the mean, mode, median, range, standard deviation (SD), and relative standard deviation (RSD) of the number of verses per chapter of Meccan, Madinite, and both type of chapters.

 

Table (3). Statistics of the number of verses per chapter in the Qur'an

	Meccan	Madinite	Total
Mean	53.64	57.96	54.70
Mode	4, 6	11, 14	5, 8
Median	43	29	39
Range	224	283	283
SD	47.49	66.98	52.98
RSD %	88.5	115.6	96.9

 

The mean number of verses per chapter for the Madinite chapters (57.96 + 66.98) is higher than those of the Meccan (53.64 + 47.49) and the total (54.70 + 52.98). The mode (bimodal), range, and RSD percentage are also the highest, while the median is the lowest. The rounded number of verses per chapter in the Meccan, Madinite and whole Qur'an is 54, 58, and 55, respectively.

 

Figure (1a) shows a pie chart of the percentage, rounded to the nearest integer, of the Meccan (75%) and Madinite (25%) chapters in the Qur'an.

 

Fig (1a). The rounded percentage of the Meccan and Madinite chapters in the Qur'an

 

Figure (1b) shows a pie chart of the percentage, rounded to the nearest integer, of Meccan (74%) and Madinite (26%) verses in the Qur'an. This is very close to the rounded percentage of the Maccan and Madinite chapters in the Qur'an. The actual difference is only 1.5%.

 

Fig (1b). The rounded percentage of the Meccan and Madinite verses in the Quran

 

The length of verses varies from a single word (e.g. 101.1) to more than 125 words (e.g. 2.282). Using the number of lines in the printed Qur'an to estimate the length of Meccan and Madinite verses, we found that 60.8% of the Quran was revealed in Mecca and 39.2% was revealed in Madina.

 

Fig (1c). The rounded percentage of the length of the Meccan and Madinite parts the Qur'an

 

While only about a quarter of the Qur'anic chapters and verses were revealed in al-Madina, because the Madinite verses are on average longer than the Maccan ones, the Madinite chapters occupy about 39% of the pages of the Qur'an.

 

The scatter graphs in Figures (2a), (2b), and (2c) show the correlation between the serial number of the Qur'anic chapters and the number of verses for these chapters in the whole Qur'an, the Meccan chapters, and the Madinite chapters, respectively.

 

Fig (2a). Number of verses in all Meccan and Madinite chapters

 

Fig (2b). Number of verses in the Meccan chapters

 

Fig (2c). Number of verses in the Madinite chapters

 

The general pattern is that the number of verses decreases as the chapter number increases. It is a negative, non-linear correlation. The Madinite chapters have the highest number of verses (286 verses in chapter 2), whereas the highest number of verses in the Meccan chapter is 227 in chapter 26. Both kinds of chapters have 3 as the lowest number of verses in a chapter -- Meccan chapters 103 and 108, and Madinite chapter 110.

 

III. The Sequential Grouping Scheme
Using Table (1), we can put together every group of consecutive chapters that were all Meccan or Madinite. After the opening chapter, which was revealed before the Hijra, there are four Madinite chapters, which are followed by two Meccan chapters, and so on. As shown in Table (4), this scheme yields 25 groups - 13 Meccan and 12 Madinite. The first, last, and middle (i.e. 13th) groups are all Meccan.

 

Table (4). The number of chapters and verses in each group of the sequential grouping scheme

Group number	Type	Number of hapters	Number of verses
1	M	1	7
2	H	4	782
3	M	2	371
4	H	2	204
5	M	3	343
6	H	1	43
7	M	8	845
8	H	1	78
9	M	1	118
10	H	1	64
11	M	8	678
12	H	1	73
13	M	13	939
14	H	3	85
15	M	5	271
16	H	1	78
17	M	1	96
18	H	10	166
19	M	9	350
20	H	1	31
21	M	21	508
22	H	2	16
23	M	10	67
24	H	1	3
25	M	4	20

 

Figures (3a) and (3b) show the number of chapters and verses, respectively, versus group numbers in the 25 groups. Figure (3c) shows the number of verses versus the number of chapters in each group.

 

Fig (3a). The number of chapters in each group versus the group numbers

 

Fig (3b). The number of verses in each group versus the group numbers

 

Fig (3c). The number of verses versus the number of chapters in each group

 

The statistical summary of the number of chapters and verses in the 25 groups is given in Table (5). It should be noted that the mode of the number of verses was taken for intervals of 100 verses each.

 

Table (5) Statistical Results for the 25 groups of chapters.

Parameter	Chapters	Verses
Mode	1	1-100
Median	2	96
Range	20	936
Mean	4.56	249.44

 

The rounded mean of the number of chapters per group is 5, and the rounded mean of the number of verses per group is 250.

 

IV. Mir's Grouping Scheme
Muntasir Mir suggested an interesting grouping scheme in his article Is The Qur'an A Shapeless Book?. Mir divided the chapters into seven groups. His logic of classification is expressed as follows: "Each group contains one or more Maccan chapters followed by one or more Madinite chapters of the same cast. Like individual chapters or each pair of chapters, each group has a central theme which runs through all its chapters, knitting them into a distinct body. In each group, the themes of the other groups also occur but as subsidiary themes. Each group logically leads to the next, and thus all the groups become variations on the basic theme of the Qur'an, which is: 'Allah's call to man to adopt the right path'." Table (6) shows the statistical results that I have obtained using Mir's grouped chapters.

 

Table (6). Summary of the results obtained using Mir's grouping scheme

Group number	chapters	Number of chapters	% of the total	Number of verses	% of the total	Mean number of verses per chapter
1	1-5	5	4.39	789	12.65	157.8
2	6-9	4	3.51	575	9.22	143.8
3	10-24	15	13.16	1491	23.91	99.4
4	25-33	9	7.89	751	12.04	83.4
5	34-49	16	14.04	1024	16.42	64.0
6	50-66	17	14.91	611	9.80	35.9
7	67-114	48	42.11	995	15.96	20.7
Total		114		6236
Mean		16.29		890.86

 

Group 1 has the highest mean of the number of verses per chapter. Group 2 has the lowest number of chapters and lowest number of verses. Group 3 has the highest number of verses. Group 7 has the highest number of chapters and the lowest mean of the number of verses per chapter.

 

Figures (4a) and (4b) show pie charts of the percentage of the number of chapters and the number of verses, respectively, in each of the seven groups.

 

Fig (4a). The percentage of chapters in the seven groups

 

Fig (4b). The percentage of verses in the seven groups

 

Figure (5a) shows a scatter graph of the number of chapters versus group number. The mean is 16.3 + 13.8 (RSD = 84.9%), with group 7 being the furthest from the mean.

 

Fig (5a). The number of chapters in the seven groups

 

Figure (5b) shows the total number of verses in each group. The mean is 890.9 + 292.0 (RSD = 32.8%).

Fig (5b). The number of verses in the seven groups

 

Figure (5c) shows the mean of the number of verses per chapter for each group.

 

Fig (5c). The mean of the number of verses per chapter in the seven groups

 

There is a strong linear negative correlation, with a gradient of 23.7. The linear equation of the line of best fit and the product moment correlation coefficient (R2) [10] are:

 

y = -23.651x + 181.04 R² = 0.9835

 

The last diagram, shows a clear trend for the number of verses per chapter in a specific group of chapters.

 

V. Conclusion
In this work, I have studied the statistical data of the number of chapters and number of verses in the chapters of the Holy Quran according to three grouping schemes. I have also provided data in graphical and tabular form about the structure of the Qur'an.

 

I used first the common approach of grouping the Qur'anic chapters into Meccan and Madinite, according to whether they were revealed before or after the Hijra. Nearly three quarters of the Quran, in terms of the number of chapters and number of verses, were revealed before the Hijra. The Madinite chapters and verses have higher means, modes, SD's and ranges, but lower medians than the Meccan. The rounded mean number of verses per chapter in the Quran is 55 verses per chapter. When the length of chapters is considered, by counting the number of lines in each chapter, the Meccan chapters cover 61% of the Quran and the Madinite 39%.

 

The second grouping scheme that I used split the Qur'anic chapters over 25 groups. In this grouping method, where each group is formed of consecutive chapters that are all either Meccan or Madinite, the rounded mean number of chapters per group is 5, and the rounded number of verses per group is 250.

 

I also used Mir's classification of the Qur'anic chapters into seven groups. The rounded mean number of chapters per group here is 16, and the rounded mean number of verses per group is 890. I have found a strong linear correlation between the mean number of verses per chapter and the group number.

 

Other grouping methods may also be used in the future.

 

One way of extending this work would be to use the length of verses, i.e. number of words per verse, and length of words in terms of the number of letters per word. This would be useful in extracting information about the style of writing. Another method of measuring the length of words would count the number of syllables per word, which is the method used by readability formulae.

 

Notes
[1] Mode is the most frequent number in the set.
[2] Median is a value in an ordered set of values below and above which there is an equal number of values, or the arithmetic mean of the two middle values if there is no one middle number.
[3] Range is the difference between the highest and lowest values in the set.
[4] SD (standard deviation) a measure of the dispersion of a frequency distribution that is the square root of the arithmetic mean of the squares of the deviation of each of the class frequencies from the arithmetic mean of the frequency distribution.
[5] RSD% (relative standard deviation) is the percentage of the standard deviation to the mean (RSD = SD/ Mean X 100).
[6] To facilitate reading or memorizing, the Qur'an is split into parts. It is divided into 30 equal parts each of which is known as Juzu' (part). Each part is, in turn, divided into two halves each of which is called hizb. Finally, each hizb is divided into four rub's (quarters).
[7] There are six factors for the number 114: 2, 3, 6, 19, 38, & 57. Half of the factors are prime Numbers: 2, 3 & 19. Also half of the factors are even numbers.
[8] The number 86 has two factors, 2 & 43, both of which are prime numbers.
[9] There are four factors for the number 28: 2, 4, 7, & 14. Half of these factors are prime numbers: 2 & 7.
[10] R² always lies between -1 and 1. The better the correlation the nearer it is to 1.