This online utility analyzes the digit frequency in one or more integers and prints the digit statistics to the screen. You can find the frequency distributions of one, two, three, or more digits, as well as check the Benford's law (first-digit law). You can display the digit count, percentage, and total values, and also choose the format of the output in the options. Created by math nerds from team Browserling.

This online utility analyzes the digit frequency in one or more integers and prints the digit statistics to the screen. You can find the frequency distributions of one, two, three, or more digits, as well as check the Benford's law (first-digit law). You can display the digit count, percentage, and total values, and also choose the format of the output in the options. Created by math nerds from team Browserling.

With this browser-based program, you can analyze the frequency of digit occurrences in one or more integers. It runs through all the digits in input integers and prints the information about the statistical digit distributions in them. For example, by entering the integer 242555 as input and analyzing single digits, you will get information that this value consists of two twos, one four, and three fives. If you adjust the "Digit Length" option to 2, then you'll get information about two-digit values: "24", "42", and "25" appear 1 time and "55" appears 2 times. Similarly, three-digit values "242", "425", "255", and "555" appear 1 time. To analyze all possible digit lengths, enter the asterisk symbol "*" in the option. You can also specify other digit length values by listing them separated by commas "1, 2, 5" (this will print statistics of single-digits, digit pairs, and five-digit values), using a range "2-4" (this will print statistics of two, three, and four-digit values), or by combining a list and a range "1-3, 5, 6" (this will print statistics of one, two, three, five and six-digit values). By default, the maximum digit length is equal to the longest integer in the input, but if you activate the option "Join All Integers", then the input will be concatenated and all the input values will form a single large integer. You can also quickly generate statistics to check the Benford's law (also know as Newcomb-Benford law or law of anomalous numbers). This law states that most often, the leading digit of statistics taken from real life is 1, while the greater digits 2, 3, … appear as the most significant digit less and less. To verify the first-digit law, enter a set of integer data in the input field and activate the "Anchor at Beginning" option. This option will look only at the first digit of each integer. By default, the program displays only the number of occurrences of digits in the integer, but you can also display the percentages and fractions of the total. You can also choose the analysis output format and display the information as full text, for example, "Digit 5 appears 3 times", via the colon character, for example, "5: 3", or using a dash, for example, "5 – 3". Integerabulous!

With this browser-based program, you can analyze the frequency of digit occurrences in one or more integers. It runs through all the digits in input integers and prints the information about the statistical digit distributions in them. For example, by entering the integer 242555 as input and analyzing single digits, you will get information that this value consists of two twos, one four, and three fives. If you adjust the "Digit Length" option to 2, then you'll get information about two-digit values: "24", "42", and "25" appear 1 time and "55" appears 2 times. Similarly, three-digit values "242", "425", "255", and "555" appear 1 time. To analyze all possible digit lengths, enter the asterisk symbol "*" in the option. You can also specify other digit length values by listing them separated by commas "1, 2, 5" (this will print statistics of single-digits, digit pairs, and five-digit values), using a range "2-4" (this will print statistics of two, three, and four-digit values), or by combining a list and a range "1-3, 5, 6" (this will print statistics of one, two, three, five and six-digit values). By default, the maximum digit length is equal to the longest integer in the input, but if you activate the option "Join All Integers", then the input will be concatenated and all the input values will form a single large integer. You can also quickly generate statistics to check the Benford's law (also know as Newcomb-Benford law or law of anomalous numbers). This law states that most often, the leading digit of statistics taken from real life is 1, while the greater digits 2, 3, … appear as the most significant digit less and less. To verify the first-digit law, enter a set of integer data in the input field and activate the "Anchor at Beginning" option. This option will look only at the first digit of each integer. By default, the program displays only the number of occurrences of digits in the integer, but you can also display the percentages and fractions of the total. You can also choose the analysis output format and display the information as full text, for example, "Digit 5 appears 3 times", via the colon character, for example, "5: 3", or using a dash, for example, "5 – 3". Integerabulous!

Click to try!

click me
### Digit Frequency Distribution

**Required options**

In this example, we analyze the frequency of occurrence of all single-digit values 0 to 9 in multiple integers. To do this, we enter the value "1" into the digit-length option, which corresponds to the analysis of individual digits. We display only the digit counts in the format "digit: number-of-occurrences". As you can see, the most popular digit is 5 and it appears 6 times.

23589
4561
56842
9540
807102
5250

0: 4
1: 2
2: 4
3: 1
4: 3
5: 6
6: 2
7: 1
8: 3
9: 2

Enter the lengths of digits that
you want to analyze. Use list
"1, 2, 4" or range "2-5" formats.

Concatenate multiple input
integers together and analyze
them as a single integer.

Only look at the leading digit(s)
of the input integers. (Useful
for verifying the Benford's law.)

Print the frequency of occurrence
of each digit or group of digits.

Choose the integer
statistics format
that you like.

click me
### Multi-digit Analysis

**Required options**

In this example, we analyze single-digit, two-digit, three-digit, and five-digit sub-integers. To include all of these values in the analysis, we set the analysis length option to "1-3, 5". This way the analysis algorithm looks at all sub-integers of length 1 to 3 and 5. We also activate the "Join All Integers" mode to examine both input integers as one big integer. We use the dash format for the statistics output and display the frequency of the digits together with their total count.

2454
5245

2 – 2 (2/8)
4 – 3 (3/8)
5 – 3 (3/8)
24 – 2 (2/7)
45 – 3 (3/7)
52 – 1 (1/7)
54 – 1 (1/7)
245 – 2 (2/6)
452 – 1 (1/6)
454 – 1 (1/6)
524 – 1 (1/6)
545 – 1 (1/6)
24545 – 1 (1/4)
45245 – 1 (1/4)
45452 – 1 (1/4)
54524 – 1 (1/4)

Enter the lengths of digits that
you want to analyze. Use list
"1, 2, 4" or range "2-5" formats.

Concatenate multiple input
integers together and analyze
them as a single integer.

Only look at the leading digit(s)
of the input integers. (Useful
for verifying the Benford's law.)

Print the frequency and total of
each digit or group of digits.

Choose the integer
statistics format
that you like.

click me
### Verify Benford's Law

**Required options**

In this example, we load country population statistics and verify Newcomb-Benford law. To find how often each leading digit appears in the sample data, we activate the "Anchor at Beginning" option. This option anchors the analysis at the first digit of each integer and discards other digits. This way, we get the frequency distribution of the first digit together with their percentage. We also select the option to print the statistical information in the text format. Looking at the output, we can say that this data follows the Benford law as the smallest leading digits appear often (digit 1 occurs in 40% of cases), while the larger digits are rarely found in the first spot (digit 9 occurs in only 8% of cases).

1404694000
1376404000
329957441
266911900
218481188
211819980
208170076
171049608
146748590
126577691
125950000
112079000
108988550
100791150
96208984
86791000
84342410
83154997
83149300
68859599
66647112
66545883
60238522
55890747
54956900
54045000
51780579
48258494
47564296
46934632
44938712
43053000
42792500
41660982
40006700
39310000
38313035
38206430
36006860
34342017
34218169
32918580
32710000
32225560
32162184
31825000
30418000
30366000
29162000
28609000
25795000
25717000
25680342
25666000
24348251
23782448
22314743
21803000
20870060
19658000
19618065
19401658
19256346
18763165
17861000
17679735
17563749
17522410
17469745
17070000
15948000
15443000
15288489
14645000
12771000
11952693
11722038
11476279
11469896
11333000
11215578
11062000
10911819
10741165
10739000
10693939
10670315
10315244
10313447
10276617
9981500
9771000
9722556
9408400
9158345
9136000
9127000
8902600
8776000
8570146

Digit 1 appears 40 times (40%).
Digit 2 appears 15 times (15%).
Digit 3 appears 14 times (14%).
Digit 4 appears 8 times (8%).
Digit 5 appears 4 times (4%).
Digit 6 appears 4 times (4%).
Digit 8 appears 7 times (7%).
Digit 9 appears 8 times (8%).

Enter the lengths of digits that
you want to analyze. Use list
"1, 2, 4" or range "2-5" formats.

Concatenate multiple input
integers together and analyze
them as a single integer.

Only look at the leading digit(s)
of the input integers. (Useful
for verifying the Benford's law.)

Print the frequency and percentage
of each digit or group of digits.

Choose the integer
statistics format
that you like.

You can pass input to this tool via __?input__ query argument and it will automatically compute output. Here's how to type it in your browser's address bar. Click to try!

https://onlinetools.com/integer/analyze-integers__?input__=23589%0A4561%0A56842%0A9540%0A807102%0A5250&digit-length=1&join-integers=false&anchor-at-beginning=false&print-count=true&output-format=colon-format

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