So Young, So Old

Nathan Yau at Flowing Data has produced an interactive graphic to compare your age with others. What percentage of the US population is younger than you? What percentage is older? In the static image above the US median age appears to be about 37 years old. Based on a 5-year American Community Survey from 2014, his interactive graphs lets you slide the line to match any age and see the percentage of Americans older or younger.

Nuptial Age

Flowing Data has produced an interactive graphic showing the distribution of the age of marriage of Americans. Smoothed relative frequency distributions are shown for women (in green) and men (in orange) with selections possible by employment, education, race, or whether or not it is a first marriage. The data are from the American Community Survey marriages from 2009 to 2014. My guess is that similar frequency distributions from earlier decades would have modes that move more to the left towards younger ages for both women and me. What is the overall youngest median age of marriage for Americans? More data needed.

Learning The Alphabet

Software engineer Erik Bernhardsson took a sample of 50,000 fonts, with characters as varied as shown in the compilation above, and looked for basic underlying structure with a neural network. A neural network is statistically a linear combination of nonlinear functions of linear combinations of input variables. Here, the input variables are digital images of each font character expressed as vectors. Iterative adjustment, termed learning, is applied to produce a linear combination of the inputs. An output estimate of the input character is computed from the other set linear coefficients. All coefficients are chosen to minimize a measure of lack of fit. Bernhardsson then looked at the mean and median of the resulting output characters.

Mean of all the output fonts.

Median of all the output fonts.

Note how readable the mean and median fonts are, when the individual input fonts are extremely varied, as shown above in the first image. He goes on to interpolate fonts, apply random perturbations, and even generate new fonts by sampling from a multivariate normal distribution of the font vectors. 

A mean of a collection of fonts we have seen before using a technique of simple visual averaging.

Taller still

More evidence that, on average, men are taller than women, (late vacation find).

Happiness in Negative Space

This image is from an Institute of Contemporary Art, Philadelphia exhibit called The Happy Show by Stefan Sagmeister that just ended its tour at the Institute of Museum of Contemporary Art, Los Angeles Pacific Design Center. In this display, included in the exhibit, people were instructed to select one gumball from column that indicated their level of happiness (1 to 10). The bar chart of the happiness level of those that participated is shown in the negative space above each column, showing how many gumballs were removed. Median happiness here looks to be about a 7. We've seen a similar exhibit before.

Market Price

Market Price (getmarketprice.com) collects the current prices of items (over $100) selling on e-bay. It provides summary statistics (min, max, median, mean, and standard deviation) along with a histogram of prices and a scatterplot of  time left to bid against price. They also include a list of the raw data with links.

A Pearl: a Balanced Median Necklace

The September issue of The College Mathematics Journal has this balance point view of the median by Mark Lynch of Millsaps College.