# Quality Progress - September 2017 - 52

```Statistics Spotlight
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124345464755497541275299949514654237204317
91545154134541213231315447133415341545721157945495241262
124345464755497541275299949514654237204317
91545154134541213231315447133415341545721157945495241262
124345464755497541275299949514654237204317
91545154134541213231315447133415341545721157945495241262

additional complexity resulting from
gravity that varies due to location or
air resistance, more complications
that are encountered in real-world
problems could be added after I had
mastered basic penguin ballistics.
A typical example from my physics
textbook is: "A football is kicked at
an angle θ₀ = 37.0° with a velocity of
20.0 m/s ... Calculate (a) the maximum height, (b) the time of travel
before the football hits the ground,
(c) how far away it hits the ground,
(d) the velocity vector at the maximum height and (e) the acceleration
vector at maximum height. Assume
the ball leaves the foot at ground
level." 1
Kicking a penguin sounds excessively cruel, so my tutors would
begin with, "Suppose we have a penguin at the equator in a vacuum and
we impart a force of 20.0 m/s to the
penguin. To determine the maximum
height, we must ..."
With the basic understanding
I gained based on penguin-related examples, I could later easily
convert a textbook problem to my
more-comfortable world of penguins
and perform the calculations. The
same principles apply when going
from penguins or textbooks to
real-world situations. I just need to
start factoring in things such as air
resistance.

Simple models for
complex problems

Using a simplified model can be
advantageous when communicating
a new and potentially nonintuitive
concept, learning new concepts or
attempting to understand a complex
real-world phenomenon.
Dianna Cowern asks, "What would
happen if a rock is dropped from a
boat?"2 Would the water level go up

52 QP

September 2017 ❘ qualityprogress.com

With the basic understanding I gained based
on penguin-related examples, I could later
easily convert a textbook problem to my more
comfortable world of penguins and perform
the calculations.

or down? Take a moment and think about that before
moving to the next paragraph.
Naturally, the water level would go down because
the rock is displacing its weight while in the boat, but it
displaces an area equivalent to its volume when it is in
the water. That simple answer may not be so intuitively
grasped by everybody, but it can be easily explained
using a simple thought model.
Suppose somebody is in a boat with a 1,000 kg marble that only has a diameter of 2.4 cm. The boat will sit
lower in the water due to the 1,000 kg of weight. After
the marble is in the water, the boat will rise because its
total weight is now 1,000 kg less. The marble will enter
the water and displace a volume of water equivalent to
its actual size resulting in the water level going down
compared to when the marble was in the boat.
The example with the unrealistic marble is an easier
concept to grasp than the more realistic rock example.
But anybody who can understand the simplified model
should be able to understand the same principles when
applied to an actual situation.
Models have a place in statistics, whether as a
thought experiment (that is a model) for explaining a
concept or as a mathematical model of the world.

Models and explanations

A typical probability example from a statistics text
book is the tossing of a coin such as "the probability of
getting either a head or a tail on a toss is one, and there
is a 50% chance of a head and a 50% chance of a tail."3
That book and many others like it are intended for
teaching statistics to future engineers, yet they use
examples related to coins, cards and dice. This does not
imply that a knowledge of gambling or games is necessary for applying statistical concepts. These examples
are simplified models intended for teaching the basics
of a concept, much like the penguin-related examples
used for teaching physics.
Often, statistics textbooks have some variation of

```
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# Table of Contents for the Digital Edition of Quality Progress - September 2017

Seen and Heard
Progress Report
Mr. Pareto Head
Career Coach
Expert Answers
Field Notes
Data Disruption
The Deal With Big Data
Better Intelligence
A Study in Measurement
Innovation Imperative
Statistics Spotlight
Standard Issues
ASQ's 2017 Quality Resource Guide
Marketplace
Footnotes
Back to Basics
Quality Progress - September 2017 - Intro
Quality Progress - September 2017 - cover1
Quality Progress - September 2017 - cover2
Quality Progress - September 2017 - 1
Quality Progress - September 2017 - 2
Quality Progress - September 2017 - 3
Quality Progress - September 2017 - 4
Quality Progress - September 2017 - 5
Quality Progress - September 2017 - Seen and Heard
Quality Progress - September 2017 - 7
Quality Progress - September 2017 - Progress Report
Quality Progress - September 2017 - 9
Quality Progress - September 2017 - Mr. Pareto Head
Quality Progress - September 2017 - 11
Quality Progress - September 2017 - Career Coach
Quality Progress - September 2017 - 13
Quality Progress - September 2017 - 14
Quality Progress - September 2017 - Expert Answers
Quality Progress - September 2017 - Field Notes
Quality Progress - September 2017 - 17
Quality Progress - September 2017 - 18
Quality Progress - September 2017 - 19
Quality Progress - September 2017 - Data Disruption
Quality Progress - September 2017 - 21
Quality Progress - September 2017 - 22
Quality Progress - September 2017 - 23
Quality Progress - September 2017 - 24
Quality Progress - September 2017 - 25
Quality Progress - September 2017 - The Deal With Big Data
Quality Progress - September 2017 - 27
Quality Progress - September 2017 - 28
Quality Progress - September 2017 - 29
Quality Progress - September 2017 - 30
Quality Progress - September 2017 - 31
Quality Progress - September 2017 - 32
Quality Progress - September 2017 - 33
Quality Progress - September 2017 - Better Intelligence
Quality Progress - September 2017 - 35
Quality Progress - September 2017 - 36
Quality Progress - September 2017 - 37
Quality Progress - September 2017 - 38
Quality Progress - September 2017 - 39
Quality Progress - September 2017 - 40
Quality Progress - September 2017 - 41
Quality Progress - September 2017 - A Study in Measurement
Quality Progress - September 2017 - 43
Quality Progress - September 2017 - 44
Quality Progress - September 2017 - 45
Quality Progress - September 2017 - 46
Quality Progress - September 2017 - 47
Quality Progress - September 2017 - Innovation Imperative
Quality Progress - September 2017 - 49
Quality Progress - September 2017 - 50
Quality Progress - September 2017 - Statistics Spotlight
Quality Progress - September 2017 - 52
Quality Progress - September 2017 - 53
Quality Progress - September 2017 - Standard Issues
Quality Progress - September 2017 - 55
Quality Progress - September 2017 - 56
Quality Progress - September 2017 - 57
Quality Progress - September 2017 - ASQ's 2017 Quality Resource Guide
Quality Progress - September 2017 - 59
Quality Progress - September 2017 - 60
Quality Progress - September 2017 - 61
Quality Progress - September 2017 - 62
Quality Progress - September 2017 - 63
Quality Progress - September 2017 - 64
Quality Progress - September 2017 - 65
Quality Progress - September 2017 - 66
Quality Progress - September 2017 - 67
Quality Progress - September 2017 - Marketplace
Quality Progress - September 2017 - 69
Quality Progress - September 2017 - Footnotes
Quality Progress - September 2017 - 71
Quality Progress - September 2017 - Back to Basics
Quality Progress - September 2017 - cover3
Quality Progress - September 2017 - cover4
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