how are quantitative observation and measurment related?

Answer 1

Quantitative anything means it has measurable, countable, or observable value. Six shoes is a quantitative observation because we have a value N = 6 shoes. We didn't measure 6 shoes because we used no metric device (like a meter stick or a balance scale) with standard, agreed to units of measure (like meter or pound). We just looked at them...we observed and counted them. That's a quantitative observation.

We might weigh the six shoes using a bathroom scale and find that W = 12 pounds for the six shoes altogether. The 12 is a quantitative value using a measurement; the pounds indicates the standard unit of measure used to get the measurement of 12 pounds.

Because measurements result in quantitative values, we can say measurements are quantitative observations that use standard metrics for measuring. But, as we saw earlier, not all quantitative observations (like N = 6 shoes) are measurements because not all quantitative observations use standard metrics.

The flip side is a qualitative observation, where what we see is not countable or measurable because it has no inherent value. For example, the observed shoes are brown. Brown is not countable; it has no inherent value. In fact it is a largely subjective color; what is brown to you may be maroon to me. Brown shoes is a qualitative observation.