**"In 1937 the Median Age of Orchestra Audiences was 30"**

As a part of the National Orchestral Survey in 1937, Margaret Grant and Herman S. Hettinger published audience survey data from the LA Philharmonic and the Grand Rapids Symphony Orchestra. The median age of the audiences from the two surveys was included in their book, "America's Symphony Orchestras," published by W.W. Norton in 1940.

## ClaimEdit

Symphony audiences in 1937 were significantly younger than today's symphony audiences showing that the age of orchestra audiences wasn't always old. This claim is debatable and probably false, but the claim that the median age of orchestra audiences in 1937 is 30 is undecidedly false.

FALSE

## ExamplesEdit

*"In 1937, the average age of the orchestra audience apparently was — believe it or not! — about 30."*(Sandow, 2006)

*"How young the audience was in 1937: Results of an audience study, showing a median age around 30."*(Sandow, 2011)

*"But in fact every study I've seen from the past shows a young audience, no older, in fact, than the population at large, with a median age (at least before the 1960s) not much over 30. This includes studies done in Minneapolis in 1955, and in Los Angeles and Grand Rapids."*(Sandow, 2013)

*"In 1937, a study of classical music audiences in America yielded a median age of 30."*(Rao, 2014)

### VariantsEdit

*"Sandow notes that back in 1937, the median age at orchestra concerts in Los Angeles was 28. Think of that!"*(Vanhoenacker, 2014)

## DiscussionEdit

The median age of the LA Philharmonic audience was 33. The median age of the Grand Rapids Symphony was 27. The median of the medians is 30 which is not the same thing as saying the median age of both audiences is 30.

For example, let's say the median age of the LA Phil were composed of two persons, one aged 32 and one aged 34 (= median age of 33) and the median age of the GRS were composed of two persons, one aged 22 and one aged 32. The median age of all audience members of both groups would be 32. A median age of 32 or any other median age which can be constructed has no relationship to the median of the median ages, which is 30. We need to have all ages from both populations to accurately construct the median age of the population of both groups as a whole.

This, of course, doesn't tell us about the median age of orchestra audiences since these samples are (1) relatively small samples, (2) self selected --i.e. not randomly selected samples, (3) include a wide degree of variance which also may or may not be representative of the variance of all symphony audiences.

Extrapolating meaningful information from from unrepresentative samples to show some sort of relationship regarding the purported rising median age of orchestra audiences is problematic at best and disingenuous otherwise. The particular usage above shows an obvious misunderstanding of how a simple concept like averages are used in statistics.

### Funnel Plot DistributionEdit

Given that there are some two dozen similar audience survey studies with a wide variety of median ages from individual orchestras also shows that in conjunction with the larger audience and participation surveys (e.g. McKinely, NEA SPPA, NIA, Baumol), which show a much older audience, we should have a characteristic funnel plot showing a classic distribution of ages with largest studies being near the average, and smaller studies spread on both sides of the average. Indeed, we can see that well well before many of the current SPPA which have shown a rising median age, two separate surveys from the Minnesota Orchestra in 1985 and 1989 show a median age for audiences that is significantly higher (48 and 51, respectively) than the SPPAs from near those periods (1982=40, 1992=45) and even later (2002=49).

That there is a rising median age isn't in doubt. We would expect that given the rising median age of the US population as a whole. That the median age of orchestra audiences is rising faster than the median age of the population as a whole is also to be expected since we can also see from the largest surveys that the rate of rise of orchestra audience's median age is proportional to rate of rise of the population's median age. That proportional rate fits perfectly well with other data we have for rising median age for marriages and rising age for first births. What makes this particular claim contentious is that, if true, then a case could be made for a rising rate that is happening at a much faster rate than simple proportional rise would have us expect. Fortunately, the median of medians of 30 is not the same as a median age of 30, and the unrepresentative sample shows a wide range without being a complete (i.e. random sampling) expression of the actual range.

## NotesEdit

It should be noted that an audience survey for the Harrisburg Pennsylvania Symphony was also conducted but not discussed in the Grant and Hettinger Book so there is no way to see which of the two median ages might be an outlier though it might be the case that the Harrisburg sample was the outlier.