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Center, spread, and shape of distributions — Harder example

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- [Instructor] A store has five different lengths of extension cords for sale, as shown in the table above. If the range of lengths of the five cords is 7 feet, what is the greatest possible value of x? So the range is the difference between the highest value and the lowest value, and if we're trying to find the greatest possible value of x, then x should be the greatest value here. Let's see if that can work out. So let's just write the cord lengths. And I just like to write 'em in order just to visualize things. So let's see. The lowest one is six feet. And then we have a seven-foot cord. Then we have an eight-fort cord. And then we have an 11-foot cord. And then we have the x-foot cord, but let's not think about that one just yet. So if these were just the four types of cords, the range here would be the high minus the low. It would be 11 minus six, which is equal to five. Now they tell us that the real range is seven feet, so that means we can go even higher than 11. And one way to think about it is, if we're tryna maximize the value for, if we need to maximize the value for x, then we need to go seven higher than the lowest value. So the lowest value is six. You go seven higher than that, so plus seven, you're going to get to 13. So x, the highest possible value for x is 13. So x would be equal to 13. So x is 13 right over here. Now if someone were to say what would be the lowest possible value for x, you'd wanna go the other way around, so that there's six, seven, 18, and 11, and if you wanted the minimize the value for x, you wanna make x as small as possible, then you would say, okay, well x is going to be the minimum of our cord lengths, and then you would take seven less than the highest. So 11 minus seven, 11 minus seven is going to get you to four. So this question says what's the highest possible value of x? It's 13. But if it said what's the lowest possible value of x? Then it would be the high, the existing high, minus seven, so that you can get a range of seven. And so in that case you would have gotten four. But that's not what they, they didn't ask us this. I'm just, you know, in the future you might see a question like that.