A little more than 60 years ago, a journalist named Darrell Huff wrote a book, titled “How to Lie with Statistics.” Huff was not a statistician, but his book sold more than one and a half million copies in English and it became a standard textbook in college statistics classes during the 1960‘s and 1970‘s. It has also been widely translated, the most recent edition being in Chinese, published in 2003 by the Department of Economics of Shanghai University.

From a strictly pedagogical perspective, the book could have been titled, “Introduction to Statistics,” just like a dozen other books that contained the same information. But, “how to lie” was the hook that grabbed public attention. You see, statistics don’t lie. Statisticians at reputable institutions don’t lie either. The thing about statistics that can be deceptive is how the data are presented. For example, there are three basic kinds of averages that are commonly used in statistics: mean, median, and mode.

Mean

Let’s take a population of seven (or seven million) people who are employed and earn income. We want to know the average income of the population, so we start by listing the gross income of each member of the universe. The “universe” is the total population with which we’re dealing. Simply defining the universe is, as I’ll show, one way to skew any statistical inference.

Anyway, worker No. 1 grosses $10,000 per year; No. 2 gets $12,000, No. 3, $24,000, No. 4, $28,000, No. 5, $32,000, No. 6 $32,000, and No. 7, $142,000. We obtain the mean (usually reported as the average) by adding the seven figures and then dividing by the total population that comprises the universe. So, the total income for this universe is $280,000. The mean is obtained by dividing that figure by the total number of earners in the universe, and that comes to $40,000. But, notice that — in actuality — nobody has a gross income of $40,000. And, in fact, only one person has more than that amount, while almost 86 percent earn less.

Median

The median is obtained by listing the incomes in descending order, counting up to the mid-point, and reporting that number. So, here are our seven incomes:

— $142,000

— $32,000

— $32,000

— $28,000

— $24,000

— $12,000

— $10,000

Notice that the median income is $28,000, but only about 14 percent (1/7) of the population earns that amount. Yet, median income or the median price of housing is often stated as if it were the “average” because half of our universe earns more than that and half earns less. Notice, also, that the bottom two incomes, close to 29 percent (2/7) earn considerably less, and only one person earns significantly more.

Mode

The modal average is the figure that appears most often in our column of descending (or ascending) numbers. In this case, the mode is $32,000, but slightly more than 57 percent (4/7) of the population earns less than this “average,” and the sole person who earns above the mode gets $110,000 more.

To make my point, I’ve been doing a bit of “lying” myself. Any statistician will tell you that if the sample (universe) is large, the mean, median, and mode will approximate each other. And, if you were to enroll in a college statistics course, you’d learn everything in this column during the first week of class. Imagine what a person who has taken advanced classes can do to confound the general populace!

The U.S. job situation

On Dec. 2, the Bureau of Labor Statistics reported its figures for November 2016. According to its calculations, the unemployment rate dropped to 4.6 percent, the lowest it’s been since the start of the Great Recession. To those who “want” good news, this is exactly what they’d hoped for. On the other hand, those who were looking for bad news got it; labor-force participation was only 62.7 percent, a 38-year low. So optimists can celebrate, and pessimists can take their frustrations out on a “poor economy.”

Optimists could also delight in the fact that employment in professional and business services increased by 178,000 jobs, and was averaging a year-long monthly increase of an average (in this case the mean average) of 180,000 jobs. Likewise, health-care employment increased by 28,000 in November, and over 407,000 during the past twelve months. But, the November figure was well below the 33,916 twelve-month (mean) average.

Okay, so who’s lying? Well …

No one’s lying

This is where defining the universe comes into play. Not every able-bodied person between 16 and 65 is counted as part of the universe. For example, in November there were 1.9 million people who were “marginally attached” to the labor force. This figure was 215,000 higher than it had been a year earlier. According to the Bureau of Labor Statistics, “These individuals were not in the labor force, wanted and were available for work, and had looked for a job sometime in the prior 12 months.” But, they were not counted as being unemployed because they had not looked for work during the four weeks preceding the Bureau’s survey.

In a like manner, there were 591,000 “discouraged workers” in November. These are people who believe that there are no jobs available for them or that they are not qualified for the available jobs. So, they have simply given up the job search. But, it does not include those who have never sought employment.

According to the Bureau’s report, issued Dec. 2, 2016, “The remaining 1.3 million persons marginally attached to the labor force in November had not searched for work for reasons such as school attendance or family responsibilities.” So, the truth is in the report, but it has to be sought carefully.

Naturally, people who would like others to see the picture from a certain perspective can pull whatever “truth” fits the bias and use only that. In other words, the “morality” rests with the user and distributor of the data; the data itself is neutral, and certainly not “amoral.” It is neither right wing nor left wing, but either side can use the data selectively to advance its particular goals.

In this age of social media (or even traditional sources, in some cases), people need to be skeptical about controversial stories that are reported until they check the sources of the data and their reliability. In many cases, the public may be getting some of the truth, but not all of it.

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Jim Glynn, a retired professor of sociology, can be contacted at j_glynn@att.net.