Reported and Measured Heights Listed below are self-reported h...

Question

Reported and Measured Heights Listed below are self-reported heights of males aged 16 and over and their corresponding measured heights (based on data from the National Health and Nutrition Examination Survey). All heights are in inches. First find the differences (reported height–measured height), and then use those differences to find the (a) mean, (b) median, (c) mode,

Accepted Answer

Welcome back, everyone. In this problem, the self-reported weights of adults aged 25 and over are provided below, along with their corresponding measured weights based on data from a health survey. All weights are in pounds. Calculate the differences between the reported and measured weights, then determine the mean, median, and mode using these differences. And here we have a table of the reported versus measured weight. For answer choices. A says the mean is 2.6, the median is 2.4, and the mode is 2.5. B says they are 2.4, 3 and 2 respectively. C 2.2, 3 and 1.5, and D, 2.6, 2.5, and 2.5. Now, if we're going to find the mean mode and median of the differences between the reported and measured weights, we need to figure out what those differences are, OK? So, here we have our table and let's add a third column for the differences, OK? And let's just extend that here. No, what we're gonna do is that we are going to subtract uh the measured weight from the reported weight. So, for example, for our first set of values, the reported weight is 150, the measure is 148.5. So the difference will be 1.5. For the second, the difference would be 2, OK? For the third, it would be 5. For the 4th, it's 1.5, OK, uh, for the 5th, it's 2.5. For the next one, it's 3. For the next one, it's 2.5, OK. And then it's gonna be 2 and then 2.5. And then it's going to be 3. So these are all the differences between the reported and the measured weights. Now that we have these, we can find the mean, the mode, and the media. First, to find the mean, remember that all we need to do is to add all the differences together and divide by the total number of data points. In other words, the mean is equal to the sum of the differences, OK. Divided by the number of data points which we we can tell here that we have uh 1010 weights, OK? Is that 10? Yes, it's 10. 123456789, 10. So now in this case, We're gonna, we're gonna add all of these up, all of these values, and I'll leave that to you to do, but when you do, OK, you should find that it equals 25.5 and 25.5 divided by 10 is equal to 2.55 or approximately 2.6 to 2 significant figures. So the meaning of our data set is 2.6. Next, to find a median, we can sort the differences in. Ascending order or descending order, whichever it is, we just have to sort it in order and then find a valet that's halfway through. So let's start our values here in ascending order. When we do that, we're gonna have 1.5, 1.5, OK, 22. 2.5, 3 times, OK. 32 times and then 5. To know which value is halfway between here. Well, if we notice out of our 10 values, the halfway value will be between the fifth and 6th value, and the fifth value here is 2.5 and the sixth value is 2.5. Therefore, the median. It is equal to the halfway point between 2.5 and 2.5, which it would just be 2.5 because that is, uh, those two values are the same. So the mean for a data set is 2.5. Finally, we know that the mode is the value that appears most frequently and by looking at our data set, we can also tell that the mode is 2.5. Therefore, from our differences, the mean difference is 2.6, the median difference is 2.5, and the more the difference is 2.5. If we look back at our answer choices, that means D is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

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Key Concepts

Mean

Median

Mode

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