Benford Law Case: Business analysts will have occasion to download large quantities of data (many thousands of rows of data for analysis in Excel) and to make a judgement as to the quality of that...

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Benford Law Case:


Business analysts will have occasion to download large quantities of data (many thousands of rows of data for analysis in Excel) and to make a judgement as to the quality of that data. These data can be sales forecasts from several locations, expense report numbers, sales numbers, etc. A good way to examine such data is by usingBenford’s Law. Benford’s Law is a statistical technique involving the distribution of leading digits of numbers. For example, the leading digit of “583.29” is “5.” Theleadingdigit of “1.99” is “1.” The leading digit of “.083” is “8” (Benford’s Law doesnot recognize a 0 as being a leading digit–only the numbers 1 through 9.)


Examine a statistically large data set (about 200 or more items). This data set must represent a human stimulus and response situation. For example, sales is a human stimulus and response example: a person wants food (the stimulus) and the person responds by buying groceries (sales is the response). A country’s GDP is another stimulus and response situation. Benford’s Law states that in such a data set, thedistribution of leading digits will be as below in Figure 1.


Leading Digit


1 2 3 4 5 6 7 8 9


% of Occurrences


30.10% 17.61% 12.50% 9.69% 7.92% 6.69% 5.80% 5.11% 4.58%


Figure 1


Go to the Internet and download a large number of data values regarding a human stimulus and
response situation (like sales, GDP, etc.) Please follow the example below in Figure 2. Put allthe data values that you want to examine using Benford’s Law into acolumn (the data may already be in that format). In this example, the data is in


column C. Insert a blank column to the right of that column. Then go into Excel“Formulas/Text/Left.” This is the “left string” formula. See the “Function Arguments” dialog box. The text is in cell c2 ($130,475) and the number ofcharacters from the left to be shown in cell D2 is 1.


Figure 2


Copy and past this formula down the column D. Then use a pivot table to count all of the 1, 2, 3, etc. values as in Figure 3. Convert these into percentages–for example, the leading digit of 1 occurred 60 out of 191 times, or 31.41% of the time. The leading digit of 2 occurred 34 times out of 191 total, of 17.80% of the time.


Figure 3


Benford’s Law states that in these human stimulus and response situations, the leading digit of “1” should happen about 30.10% of the time, the leading digit of “2”should happen about 17.61% of the time, etc., as shown in Figure 3’s far rightcolumn.


So, for this case,


1.Download at least about 200 rows of Excel data which reflects human stimulus and response.


2.Extract the leading digit using the LEFT formula in Excel.
3.Count the number of each leading digit.
4.Compare the percentage of each leading digit with that forecast by Benford’s Law.5.Write your conclusion of your findings.

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Answered Same DayJul 02, 2022

Answer To: Benford Law Case: Business analysts will have occasion to download large quantities of data (many...

Irfan Haider answered on Jul 02 2022
98 Votes
GDP
        Gross domestic product 2021
                    (millions of
        Ranking        Economy    US dollars)
    USA    1        United States    22,996,100
    CHN    2        China    17,734,063
    JPN    3        Japan    4,937,422
    DEU    4        Germany    4,223,116
    GBR    5        United Kingdom    3,186,860
    IND    6        India    3,173,398
    FRA    7        France    2,937,473
    ITA    8        Italy    2,099,880
    CAN    9        Canada    1,990,762
    KOR    10        Korea, Rep.    1,798,534
    RUS    11        Russian Federation    1,775,800    a
    BRA    12        Brazil    1,608,981
    AUS    13        Australia    1,542,660
    ESP    14        Spain    1,425,277
    MEX    15        Mexico    1,293,038
    IDN    16        Indonesia    1,186,093
    NLD    17        Netherlands    1,018,007
    SAU    18        Saudi Arabia    833,541
    TUR    19        Türkiye    815,272
    CHE    20        Switzerland    812,867
    POL    21        Poland    674,048
    SWE    22        Sweden    627,438
    BEL    23        Belgium    599,879
    THA    24        Thailand    505,982
    IRL    25        Ireland    498,560
    ARG    26        Argentina    491,493
    NOR    27        Norway    482,437
    ISR    28        Israel    481,591
    AUT    29        Austria    477,082
    NGA    30        Nigeria    440,777
    ZAF    31        South Africa    419,946
    BGD    32        Bangladesh    416,265
    EGY    33        Egypt, Arab Rep.    404,143
    DNK    34        Denmark    397,104
    SGP    35        Singapore    396,987
    PHL    36        Philippines    394,086
    MYS    37        Malaysia    372,701
    HKG    38        Hong Kong SAR, China    368,139
    VNM    39        Vietnam    362,638
    ARE    40        United Arab Emirates    358,869
    PAK    41        Pakistan    346,343
    CHL    42        Chile    317,059
    COL    43        Colombia    314,322
    FIN    44        Finland    299,155
    ROU    45        Romania    284,088
    CZE    46        Czech Republic    282,341
    NZL    47        New Zealand    249,992
    PRT    48        Portugal    249,886
    IRN    49        Iran, Islamic Rep.    231,548
    PER    50        Peru    223,249
    GRC    51        Greece    216,241
    IRQ    52        Iraq    207,889
    UKR    53        Ukraine    200,086    a
    KAZ    54        Kazakhstan    190,814
    HUN    55        Hungary    182,281
    QAT    56        Qatar    179,571
    DZA    57        Algeria    167,983
    MAR    58        Morocco    132,725    b
    SVK    59        Slovak Republic    114,871
    ETH    60        Ethiopia    111,271
    KEN    61        Kenya    110,347
    CUB    62        Cuba    107,352
    ECU    63        Ecuador    106,166
    KWT    64        Kuwait    105,960
    PRI    65        Puerto Rico    103,138
    DOM    66        Dominican Republic    94,243
    LUX    67        Luxembourg    86,711
    GTM    68        Guatemala    85,986
    OMN    69        Oman    85,869
    LKA    70        Sri Lanka    84,519
    BGR    71        Bulgaria    80,271
    GHA    72        Ghana    77,594
    AGO    73        Angola    72,547
    CIV    74        Côte...
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