Posted: December 7th, 2016
Q1: What are the two Branches of Statistics?
Q2: Theorize what the distributions would approximately look like for both the right-hand and left-hand digits of the populations of towns and cities from your selected state. Show a sketch in the rectangles below.
You have to choose one of three options to complete this activity. Your total score depends on the option chosen.
Option 1: Regular score (7.0 points)
Which Option did you choose?
If Option 1, which State?
Analysis: Now with both side-by-side bar graphs completed, answer the questions below.
Referring to the one you did not circle above, describe in a brief sentence what characteristic(s) of the shape made it not be the best fit.
Discussion: Before addressing the items below, modify the formula for the Left-hand
Theoretical Count by using the logarithmic formula from Benford’s Law. A brief Internet search on “Benford’s Law” and/or “first digit phenomenon” would be very helpful.
Why do you suppose the actual count distributions are not as smooth as the theoretical?
By changing the right-hand theoretical count to reflect the logarithmic formula from Benford’s Law, discuss how the shape improved the fit of the actual count
Why would the right-hand digit’s distribution be approximately uniform (flat)?
Why would the left-hand digit’s distribution be roughly right-skewed? (see #5 below)
To better understand why there is a built-in bias for the lower digits in the left-hand distribution, scan the sorted populations of your state from low to high. Discuss why a city, as it grows in population, would remain with a left-hand digit of a 1 longer than a 2, or why longer with a 2 than a 3, etc. You may come to a better appreciation for the first digit phenomenon that occurs in certain kinds of data by noting how there is a 100% increase from 1 to 2 but then a dramatically tapering percentage thereafter. Fill in the rest of the table and discuss how this might apply to population changes in a town or city.
Based on your Internet research, discuss a practical application of Benford’s Law that
interested you and why. Also, include what the Benford ratios are for digits 1 through 9.
Place an order in 3 easy steps. Takes less than 5 mins.