Benford's Law: Distribution of Numbers

Benford's Law is a phenomenon where numbers that start with one or two occur more frequently than numbers that start with seven, eight, or nine. This pattern has been observed across various categories such as molecular weights, baseball statistics, census data, company revenues, sizes of rivers, earthquake magnitudes, populations, deaths in wars, areas of counties, and stream flow data. Even bank account balances in New York follow Benford's Law, with numbers starting with one occurring 30.1% of the time and numbers starting with two occurring 17.6% of the time. In contrast, numbers starting with nine occur only 4.6% of the time, making one approximately six times as likely as nine. This distribution is considered quite remarkable.