The Difference Between Measured Values and Counted Values | Missing This in QC Level 3 Will Cause Everything Else to Collapse
The "weight" of a cookie and the "number" of broken cookies.
Both are data, but their properties are completely different.
This difference is between measured values and counted values.
In QC Level 3, these may seem like plain terms, but if you miss this, you will stumble on all subsequent graph and control chart selections.
Conversely, if you solidify this, your confusion will decrease significantly.
Let's settle this in this article.
In a nutshell
Measured values: Continuous values obtained by measuring
Counted values: Discrete values obtained by counting
The trick to judging is whether "decimals are possible."
Distinguishing with familiar examples
Let's think about a cookie factory.
Measured values (data that is measured)
Weight of one cookie ... Decimals are possible, such as 30.4g
Baking time ... 12.5 minutes is also possible
Oven temperature ... 180.3°C is also possible
Counted values (data that is counted)
Number of broken cookies ... 3 cookies. 3.5 cookies do not exist
Number of items in one bag ... 12 items
Number of complaints ... 2 cases
"3.5 broken cookies" is impossible.
But "a 30.4g cookie" is possible. This is the dividing line.
Checklist for distinguishing
When in doubt, think in this order.
Was it measured? Or was it counted?
Can it be a decimal? (30.4g → Measured value / 3.5 items → Impossible, so counted value)
What is the unit? (g, mm, ℃, minutes → Measured value / pieces, sheets, cases, people → Counted value)
Why is this distinction important?
This is the main point. It is because the tools you use later change depending on whether it is a measured value or a counted value.
When looking at graphs and distributions
Measured value → Look at the shape of the distribution with a histogram
Counted value → Look at it by number of cases or percentages (Pareto charts, etc.)
When choosing control charts (this becomes full-scale from Level 2, but the roles are asked even in Level 3)
Measured value → Xbar-R control chart, etc.
Counted value → p-chart, np-chart, c-chart, u-chart, etc.
When performing tests (Level 2 scope)
Comparing the means of measured values → t-test
Comparing the proportions of counted values → Test using normal approximation
In other words, if you get the initial classification wrong, all subsequent choices will be off.
It is not a "dull term" but a "branching point".
Common pitfalls
Here are patterns where people often stumble in exams.
Is "nonconforming product rate" a counted value?
→ Since it is a percentage derived from counting the number of broken items, it is originally counted value data. Although it becomes a decimal because it is a percentage, the point is that it is created from counted data.What about "temperature"?
→ Since it is data that is measured, it is a measured value.What about "pass/fail judgment"?
→ It is data that is counted (counted value). It is treated as a number of items.What about "the result of measuring length and judging whether it is out of specification"?
→ The original length is a measured value, but once it is counted as the number of items out of specification, it is treated as a counted value. Even at the same site, it changes depending on what you pick up as data.
The last example is the most important.
Whether it is 'measured or counted' is not determined by the nature of the object, but by what you recorded.
Summary
Variable data = measured data (decimals are possible; g, mm, °C, minutes)
Attribute data = counted data (decimals are impossible; pieces, sheets, cases)
If you are unsure, judge by whether it 'can be a decimal'
This distinction is the gateway to selecting all graphs, control charts, and tests
Even at the same site, it can be either variable data or attribute data depending on 'what was recorded'
If you solidify this, the number of times you get lost wondering 'which tool should I use?' in your future studies will decrease drastically. It is an investment worth making at the beginning.
If this article was helpful, letting me know with a 'like' would be encouraging. I plan to explain how to use the Seven QC Tools and how to choose control charts using similar familiar examples. Please follow me and stay tuned.