EDIT: it's become clear to me that you either 1) confused the
units from my original iPhone formula for
values or 2) don't understand the difference between units and values. I get that from your
reply here about terms canceling out, and
this reply where you simplify the formula by replacing my units with a, b, c, and d, and later call 'a' a value. I demonstrate the difference to great detail with the following.
Oh for the love of Apple… You have bolded s/h not s/s! Please, take some time to understand what I've done before responding with another argument.
If you had included units, maybe it would have made sense.
Let me go through this step by step:
343 m / 1 s * 3600 s / 1 h * 0.00062137 miles / 1 m = 767 miles/hour
Rearrange the denominators using the commutative property:
343 m / 1 m * 3600 s / 1 s * 0.00062137 miles / 1 h = 767 miles/h
Since all the operations are multiplication, you can multiply (or divide) them in any order. Move the denominators so values are grouped by units. Cancel units:
343 m / 1 m * 3600 s / 1 s * 0.00062137 miles / 1 h= 767 miles/h
You'll notice that the term that includes seconds is 3600/1,
not 3600/3600. Now combine the unitless terms:
1234800 * 0.00062137 miles / 1 h = 767 miles/h
Finally, carry out the operation:
767 miles / 1 h = 767 miles/h
If you recall how you "simplified" my original equation:
That's the same as writing:
a/b * c/c * d/d = a/b
Now c/c = 1, and d/d = 1, so your formula just becomes:
a/b = a/b
When you did this, you improperly assigned variables to the
units (i.e. seconds = c). The key difference is that while two different values can have the same units, two different values can
not be expressed by the same variable.
At some point, you confused a, b, c, and d for values, not units. Or perhaps you didn't realize that in my original iPhone equation, "# calls", "iPhone with issue", etc. represented units, not values?
When c is a unit, then 1 is also considered a unit in the equation c/c = 1. A unit of 1 is called
unitless. That does not indicate that the actual value that carries that particular unit is 1.
That's why I stated this in response to your simplified equation many posts ago:
Your simplification is valid only in terms of units, not for the values.
If you recall my original iPhone equation:
X ("iPhone with issue"/"users who report issue") * Y ("users who report issue"/"# calls") * Z ("# calls"/"total iPhones") = G ("iPhone with issue"/"total iPhones")
...X, Y, and Z are the values. Everything in quotes within the parenthesis are units. To properly simplify this equation by replacing the units with a, b, c, and d is to do like so:
X (a/c) * Y (c/d) * Z (d/b) = G (a/b)
...where X, Y, Z, and G are the values and a, b, c, d are the units. To properly group the terms with the same units, you first have to divide terms by 1 so you can show the units on the bottom:
X (a) /1 (c) * Y (c) /1 (d) * Z (d)/1 (b) = G (a/b)
Now you can properly group terms with the same units by moving the denominators and you will see what happens:
X (a) * Y (c) /1 (c) * Z (d)/1 (d) * 1 / 1 (b)= G (a/b)
We no longer have to explicitly account for the 1 in the denominators, so we can remove them:
X (a/b) * Y (c/c) * Z (d/d) = G (a/b)
At this point, you made the mistake of confusing 'c' and 'd' as values to state that the middle terms cancel out, leaving you only with a/b = a/b. Instead, the fact that c/c = 1 indicates that the middle terms are
unitless. As you can see, the values of these terms are still indicated by the variables Y and Z.
At this point we can drop the units which have canceled and we are left with:
X (a/b) * Y * Z = G (a/b)
Finally, you can combine terms so you end up with:
X*Y*Z (a/b) = G (a/b)
Now, this is same conclusion you reached when you stated that a/b = a/b. As you say,
Not very useful for determining the unknown value of 'a'!
'a' is not a value, however. It's the unit of the value we are interested in. The
actual unknown value is G, so the final equation does become useful in determining it as long as we know the values for X, Y, and Z.
The heart is that Apple used statistics in a misleading manner by reporting Z as if it were G, when in fact G is the product of XYZ, meaning that their figure for "G" is off by a factor of XY.