During the 1950s, it was a common observation among graduate students in math that statistics don’t lie, statisticians figure. They figure the numbers and then they figure what the numbers mean. The first is mathematics. The second requires human judgment that brings assumptions and biases with it. The mathematics may be rigorous, but what the numbers mean is still an opinion.
We are inundated with statistics. The government tells us the rate of inflation, how much Americans earn, how many people are employed or unemployed, how many Americans live in poverty, what homes cost, how much consumers spend and whether the economy is growing or shrinking. These numbers are reported by newspapers and television commentators with remarkable precision and usually with very little explanation of where they came from. Put a percentage sign after a number and identify a federal agency as its source and the number acquires an almost mystical authority. But it shouldn’t.
A Statistic Is the End of a Process
Every statistic begins with decisions. What information will be collected? From where? Who or what will be included? Who or what will be excluded?
There is also a problem with how a statistic is reported. A percentage is simply a fraction expressed in hundredths and its denominator tells us the size of the total group from which the percentage was calculated. Before believing any statistic expressed as a percentage, find the denominator of the fraction that became the percentage. Who or what was counted?
Surveys Are Only Estimates
Many statistics begin with a survey. Instead of counting an entire population, researchers use sophisticated mathematics to transform the answers of a relatively small number of people into a statistic purporting to describe millions of Americans.
The reliability of the resulting statistic depends upon who was selected, who responded and whether those people actually represent the population the statistic claims to describe. Sophisticated mathematics cannot make the wrong sample representative of the right population.
The question itself can also affect the result. Ask Americans whether they are “doing okay financially” and two people with identical incomes and expenses may give opposite answers because they understand “doing okay” differently. The survey has not measured their financial condition. It has measured their answers to a subjective question. Those answers can nevertheless be weighted, converted into percentages and reported to one decimal place, giving an estimate the appearance of scientific precision.
Who Was Actually Counted?
A statistic can be mathematically correct and still be misleading because it describes the wrong population. Before accepting what a statistic purports to tell you about Americans, workers, families or consumers, determine exactly who was included in the population being measured.
When the government reports median household income, it may contain the earnings of two or more people, so you cannot compare household income with the earnings of an individual worker and pretend that the two numbers describe the same economic unit. A household is not a worker. A family is not a household. An adult is not necessarily a worker. These distinctions matter.
A major bank may analyze the financial records of millions of its customers, but every person in that enormous database is a customer of the bank. What about the worker who cashes a paycheck without maintaining a substantial banking relationship? What about someone who pays bills with money orders? What about people operating primarily in cash? They may be precisely the people you need to know about when studying the economic condition of lower-income Americans, and they may be missing from the database. A sample of ten million members of the wrong population is still a sample of the wrong population.
Numbers create the appearance of authority. A statement about 52.7 percent of Americans sounds scientific, yet the decimal point proves nothing. A precisely calculated percentage derived from a biased sample remains biased. A precisely calculated estimate based upon subjective answers remains subjective.
A precisely calculated number based upon the wrong population answers the wrong question precisely.
“Government” Statistics
Some government information comes from legally required administrative reports. Some comes from surveys. Some comes from statistical samples of administrative records. Some consists of modeled estimates. Some involves assumptions or estimated values substituted for missing information. Different agencies also create technical definitions for words that ordinary Americans believe they already understand.
“Income” may not mean what you think income means. “Earnings” and “income” may not mean the same thing. “Household” and “family” may describe different populations. “Employment,” “unemployment,” “poverty” and “inflation” are statistical concepts whose government definitions may be considerably more complicated than their meanings in ordinary American English.
Even actual administrative records have limitations. An enormous government database may contain actual earnings reported by employers and self-employed individuals. Those administrative records provide a much stronger factual foundation than asking people in a survey what they earned. But what about money that was never reported? Cash wages paid off the books do not magically appear in a government database. Neither does unreported self-employment income. Workers in the underground economy may actually earn money that no government earnings statistic can observe. Even an extraordinarily large and carefully maintained government database may accurately report everything contained within it while failing to describe everything really occurring. The important question is who and what are missing from the data.
That means the statement “according to the government” should be the start of an inquiry.
Government Publication Is Not Verification
Government statistics are not necessarily wrong, but you should not believe a statistic merely because the government published it. Nor should you believe a statistic from a university, a bank, a corporation, a think tank or an organization whose politics happen to agree with yours.
Ask what the statistic actually measures. Ask who was measured. Ask who was excluded. Ask where the underlying information came from. Ask whether it represents actual transactions, administrative records, a survey, a statistical sample, a model or somebody’s answer to a subjective question. Ask how the important terms were defined. And finally ask whether the statistic actually proves anything.
Government statistics can contradict everyday experience. The federal government can announce an inflation rate, but you buy groceries. You pay an electric bill. You buy gasoline. You insure your home and automobile. You pay rent or a mortgage. You buy clothing and household necessities. You pay medical bills and insurance premiums. When the government’s description of the economy seems inconsistent with what you actually experience, ask what exactly the government measured and how they measured it. Then decide whether the government statistic answers the question that matters to you.
Statistics Are Interpretations of Data
Statistics can be extraordinarily useful. They can identify patterns within masses of data and help us understand our society and the economy beyond personal experience. But a statistic is derived from underlying data. A statistic is the result of applying mathematical methods, assumptions and human judgment to data.
Whenever someone tells you that “the statistics show” something is true, ask what data produced the statistic, who or what those data represent, and how the data were transformed into the conclusion you are being asked to accept. Then remember the warning: statistics don’t lie, statisticians figure.
Why Should You Believe Government Statistics?
September 10, 2026 | Curbstone Opinions
During the 1950s, it was a common observation among graduate students in math that statistics don’t lie, statisticians figure. They figure the numbers and then they figure what the numbers mean. The first is mathematics. The second requires human judgment that brings assumptions and biases with it. The mathematics may be rigorous, but what the numbers mean is still an opinion.
We are inundated with statistics. The government tells us the rate of inflation, how much Americans earn, how many people are employed or unemployed, how many Americans live in poverty, what homes cost, how much consumers spend and whether the economy is growing or shrinking. These numbers are reported by newspapers and television commentators with remarkable precision and usually with very little explanation of where they came from. Put a percentage sign after a number and identify a federal agency as its source and the number acquires an almost mystical authority. But it shouldn’t.
A Statistic Is the End of a Process
Every statistic begins with decisions. What information will be collected? From where? Who or what will be included? Who or what will be excluded?
There is also a problem with how a statistic is reported. A percentage is simply a fraction expressed in hundredths and its denominator tells us the size of the total group from which the percentage was calculated. Before believing any statistic expressed as a percentage, find the denominator of the fraction that became the percentage. Who or what was counted?
Surveys Are Only Estimates
Many statistics begin with a survey. Instead of counting an entire population, researchers use sophisticated mathematics to transform the answers of a relatively small number of people into a statistic purporting to describe millions of Americans.
The reliability of the resulting statistic depends upon who was selected, who responded and whether those people actually represent the population the statistic claims to describe. Sophisticated mathematics cannot make the wrong sample representative of the right population.
The question itself can also affect the result. Ask Americans whether they are “doing okay financially” and two people with identical incomes and expenses may give opposite answers because they understand “doing okay” differently. The survey has not measured their financial condition. It has measured their answers to a subjective question. Those answers can nevertheless be weighted, converted into percentages and reported to one decimal place, giving an estimate the appearance of scientific precision.
Who Was Actually Counted?
A statistic can be mathematically correct and still be misleading because it describes the wrong population. Before accepting what a statistic purports to tell you about Americans, workers, families or consumers, determine exactly who was included in the population being measured.
When the government reports median household income, it may contain the earnings of two or more people, so you cannot compare household income with the earnings of an individual worker and pretend that the two numbers describe the same economic unit. A household is not a worker. A family is not a household. An adult is not necessarily a worker. These distinctions matter.
A major bank may analyze the financial records of millions of its customers, but every person in that enormous database is a customer of the bank. What about the worker who cashes a paycheck without maintaining a substantial banking relationship? What about someone who pays bills with money orders? What about people operating primarily in cash? They may be precisely the people you need to know about when studying the economic condition of lower-income Americans, and they may be missing from the database. A sample of ten million members of the wrong population is still a sample of the wrong population.
Numbers create the appearance of authority. A statement about 52.7 percent of Americans sounds scientific, yet the decimal point proves nothing. A precisely calculated percentage derived from a biased sample remains biased. A precisely calculated estimate based upon subjective answers remains subjective.
A precisely calculated number based upon the wrong population answers the wrong question precisely.
“Government” Statistics
Some government information comes from legally required administrative reports. Some comes from surveys. Some comes from statistical samples of administrative records. Some consists of modeled estimates. Some involves assumptions or estimated values substituted for missing information. Different agencies also create technical definitions for words that ordinary Americans believe they already understand.
“Income” may not mean what you think income means. “Earnings” and “income” may not mean the same thing. “Household” and “family” may describe different populations. “Employment,” “unemployment,” “poverty” and “inflation” are statistical concepts whose government definitions may be considerably more complicated than their meanings in ordinary American English.
Even actual administrative records have limitations. An enormous government database may contain actual earnings reported by employers and self-employed individuals. Those administrative records provide a much stronger factual foundation than asking people in a survey what they earned. But what about money that was never reported? Cash wages paid off the books do not magically appear in a government database. Neither does unreported self-employment income. Workers in the underground economy may actually earn money that no government earnings statistic can observe. Even an extraordinarily large and carefully maintained government database may accurately report everything contained within it while failing to describe everything really occurring. The important question is who and what are missing from the data.
That means the statement “according to the government” should be the start of an inquiry.
Government Publication Is Not Verification
Government statistics are not necessarily wrong, but you should not believe a statistic merely because the government published it. Nor should you believe a statistic from a university, a bank, a corporation, a think tank or an organization whose politics happen to agree with yours.
Ask what the statistic actually measures. Ask who was measured. Ask who was excluded. Ask where the underlying information came from. Ask whether it represents actual transactions, administrative records, a survey, a statistical sample, a model or somebody’s answer to a subjective question. Ask how the important terms were defined. And finally ask whether the statistic actually proves anything.
Government statistics can contradict everyday experience. The federal government can announce an inflation rate, but you buy groceries. You pay an electric bill. You buy gasoline. You insure your home and automobile. You pay rent or a mortgage. You buy clothing and household necessities. You pay medical bills and insurance premiums. When the government’s description of the economy seems inconsistent with what you actually experience, ask what exactly the government measured and how they measured it. Then decide whether the government statistic answers the question that matters to you.
Statistics Are Interpretations of Data
Statistics can be extraordinarily useful. They can identify patterns within masses of data and help us understand our society and the economy beyond personal experience. But a statistic is derived from underlying data. A statistic is the result of applying mathematical methods, assumptions and human judgment to data.
Whenever someone tells you that “the statistics show” something is true, ask what data produced the statistic, who or what those data represent, and how the data were transformed into the conclusion you are being asked to accept. Then remember the warning: statistics don’t lie, statisticians figure.