Determine the level of measurement of the data listed on the h...

Question

Determine the level of measurement of the data listed on the horizontal and vertical axes in the figure.

Table displaying various times throughout the day, organized in rows and columns.

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A teacher assigns letter grades to students as A, B, C, and D. What is the level of measurement for this data set? Explain your reasoning. Awesome. So it appears for this particular problem we're asked to examine our teacher letter grade assignments, which are A, B, C, and D, and we're asked to take this particular data set, and we're asked to determine what level of measurement is used for this particular data set, and that is our final answer we're ultimately trying to solve for. And once we determine the level of measurement, we're asked to explain our reasoning for why we chose that specific level of measurement. Awesome. So now that we know what we're ultimately trying to solve for, let's take a moment to read off our multiple choice answers to see what our final answer pair might be. A isnomial and because the grades are just labels without any order, B is ordinal, and because the grades represent categories with a meaningful order, A is greater than B, B is greater than C, and C is greater than D, but the differences between them are not measurable. C is interval, and because the grades are numeric values with equal spacing between them but no true zero, and finally D is ratio and because the grades have a true zero and allow for all mathematical operations including ratios. Awesome. So now, with that in mind. Our first major step to solve this problem is we need to recall and note that there are 4 levels of measurement in statistics, which are 4 measurements, or rather I should say the 4 levels of measurement in statistics are nomial, ordinal, interval, and ratio, which will go in order the same order as our multiple choice answers and define each of them. So starting with nomial, as we should recall. No so for the nomial level, these state for categories with no inherent order, for example, hair color or gender. As for ordinal level, as we should recall, this states categories with a meaningful order, but unequal or unmeasurable intervals between them. And this, for example, would include data sets such as letter grades, satisfaction ratings. As for the interval level, as we should recall, these are numerical values with equal spacing but no true zero. An example of this particular Data set would be temperatures in degrees Celsius. And finally for ratio, these are numerical values, once again, we're talking about the ratio level. These are numerical values with equal spacing and a true zero value, which allows for meaningful ratios and examples of this particular level would be height, weight, and age, for example. And now that we've defined our 4 levels of measurement, we need to examine our given data set. So we note that we are dealing with letter grades A, B, C, and D, and they represent ordered categories with A being higher than B, etc. However, for this particular prompt, The difference between grades is not measurable or consistent. You can't say A is 2 units bigger than C. So therefore, as a result, this particular, this particular data set will have to be considered ordinal, not nomial or numerical. So that means that our correct final answer. Without a doubt, has to be multiple choice answer letter B. Which states once again ordinal and because the grades represent categories with meaningful order, A is greater than B, B is greater than C, C is greater than D, but the differences between them are not measurable. And that's it. We've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

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