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 (h) Q1, (i) Q3

Accepted Answer

Welcome back, everyone. In this problem, the self-reported weights of adults aged 25 and over, along with their corresponding measured weights and the differences between reported and measured weights are provided in the table below. All weights are in pounds. Using the differences between reported and measured weights, determine the values of the first quartile Q1 and the 3rd quartile Q3. For answer choices. A it says Q1 is 2, while Q3 is 3, B it says Q1 is 2.1 and Q3 is 3.3. C says Q1 is 2, while Q3 is 3.5, and D says Q1 is 2.5, while Q3 is 3. Now what do we know that will help us to figure out the 1st and 3rd quartet? Well, before we find the quarters, we'll need to order our data. So let's arrange the differences, OK, in ascending order. Now, when we are arranging ascending order here, that is from least to greatest, then we're gonna have 1.5, 1.5, OK? We're gonna have 2 twice. Then we're gonna have 2.5 3 times, OK. 32 times, OK. And then 5, the highest value in our data set. Let me just uh scoot this a bit to the right, to the left here, OK? So now, now that we have them in order and we can tell here that data set has 10 values, the first quartile is going to be halfway through the lower half of our values while the third quartile is going to be. Halfway through the upper half of our values, OK? So since our data set is even, if we split it into two different sides, so here, this is our lower half. OK, from 1.5 to 2.5, and then from 2.5 to 5 is going to be our upper half. Our first quartile is like we said, going to be the median. Of the median of the lower part of our data set. So now when we look here out of 5 values, the median value would be the 3rd value, which is 2. Therefore, this tells us that Q1 equals 2. On the other hand, Q3 is actually the median or the mid the middle value of the upper half of our data set data set. So if again, if we look at these five values, the value in the middle would be 3. Therefore, Q3 equals 3. Thus Q1 is 2 and Q3 is 3. When we look back at our answer choices, that tells us that A is the correct answer. Thanks for watching everyone. I hope this video helped.

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Key Concepts

Differences Calculation

Quartiles

Data Interpretation

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