One way to think about quantum operators is as Questions that are asked of a quantum system.

• Identity operator = “Who are you?”
• Energy operator = “How much do you weigh?”
• “What is your spin along the `z` axis?”
• and so on.

Statistical moments, letter values, and other verbs that are often just called “statistics” can be thought of the same way: asking questions of a data set.

For example, after you run the `∑/n` operation to get the mean happiness in Europe (2.0 / 3.0) versus the mean happiness in the US (1.2 / 2.0), you naturally would want to ask things like:

• What about the least happy people? Are there more people answering near 0.0 in the US or Europe?
• What’s the variance `√∑²/n`?
• What’s the skewness? (Blanchflower & Oswald’s data survey 45,000 Americans and 400,000 Europeans — enough degrees of freedom to meaningfully measure skew.)
• What’s the conditional value-at-risk at the 10% level? (average of the bottom 10% unhappiness.)
• Apply a smoothing kernel to pick up which country has the more least-happy people without choosing a particular cutoff. (And maybe a second kernel to deal with the different scales: should we assume `US1.0 = EUR1.5`? Or maybe count from the top, to `US1.8 = EUR2.8`?)

Running these operators on the dataset will tell you an answer to one question, just like in English.

One difference is that classical statistical operators typically spit out two numbers in reply to your question: an answer, and a confidence level in that answer. The confidence in the answer is computed based on experimental assumptions by people with names like Pearson, Fisher, and Chisquare.