Are You A Prolific Photo Poster?

Here is a shout out to all you proliferic photo posters on social media. Are you a popular photo populator? That was a rhetorical question, answer our word problem instead!

For the first six days of the week, Zoe posted three pictures per day on social media. How many does she need to post on the seventh day to have an average of four pictures posted per day for the whole week?
So, what's average?

The video above posits that our minds are always calculating the look of an average face from all the faces we see. That average face is what we expect a typical face to look like. We effectively pick a middle ground of facial features.

It's not something we consciously do, but mathematically, facial features can be modeled as a multitude of measurements, distance between eyes, eyes to nose, eyes to ears, etc. And measurements are wonderful because numbers are easily manipulated and compared. So, let's simplify the problem of what "average" means and consider a single set of numbers instead.

The average of a number set is to find a number that typifies the set. It transpires that there are 3 common ways to do this:

1. The first is to pick the number that occurs most frequently. Mathematically, this is the mode. For the fashion conscious, "mode" means style. In fashion, what is in style is what is worn the most frequently. Stylish folks "mode-l" the most common (frequent) look!
2. The second is to arrange numbers in order and pick the middle number. Mathematically, this is the median. "Median" means the middle, as in "the middle of a road is the median."
3. The third is to consider that the set of numbers consists of possibly different n-numbers. We'd like a single number for all all n-numbers. We need a number such that the sum of the set of numbers is preserved. I like to think that that one number is the mean-ing (intention) of the set. It's expressed as mean = (sum of the set) / (n-numbers in the set). The mean* is usually what we mean when we mean average!

So, with that explanation, let's solve! Zoe posts 3 x 6 = 18 photos for 6 days. On the 7th day, she has to make it appear that she's posted 4 photos per day, or 4 x 7 = 28 photos. Hence, she has to post 28 - 18 = 10 photos on the 7th day. Another way to understand that 10 photos, is to post 4 photos a day, she needs 1 extra photo for each of the first 6 days, then 4 more photos for the seventh day, a total of 6 + 4 = 10 photos.

Note that having posted 10 photos on the 7th day, Zoe's mean posting rate is 4 photos a day, but her mode posting rate is still 3 photos a day, and her median posting rate is also 3 photos a day. Which number is a better description of her photo posting predilection? Neither! It's a matter of interpretation and intent -- a huge can of worms that we're not getting into.

Math and statistics are wonderful tools, but the results must be interpreted and understood in context -- usually way more complex than the math. Like a measure of "facial beauty", math can crunch all sorts of measures of features we think are important and produce comparative numbers. We have to interpret those numbers in comparison to what our population calls "beautiful", and that's up for all sorts of disagreements that math cannot settle.

*mean originates from old French where it means "middle" and was pressed into mathematical use in 1500 to mean the average "mean".

Contact:
Ruby Yao and Benedict Zoe, Mathnasium of Fort Lee
201-969-6284 (WOW-MATH), fortlee@mathnasium.com
246 Main St. #A
Fort Lee, NJ 07024
Happily serving communities of Cliffside Park, Edgewater, Fort Lee, Leonia, and Palisades Park.