What is the formula of by shift of origin & scale method?
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Answer:
I did a search on the exact term "Mean is affected by change in origin." and came up with a 10th grade book that was online. If it's the same or similar book, it's about basic statistics, and in particular about the arithmetic mean (it's called that is it's the version of the mean that can be calculated with arithmetic.) At this point, it really doesn't have anything to do with a graph. It can be extended to things you might graph later on, but I'm trying to keep this as simple as possible.
The (arithmetic) mean x¯ is defined as x¯=(x1+⋯+xn)/n , where n is the number of measurements, which can be shortened into summation notation x¯=∑ni=1xi/n (don't let the second notation worry you, if it does. You may not have been taught it yet. I can't remember when I learned it, and I don't have time at the moment to search the book, especially since it may not be the same book.)
The word origin usually, and in this case, means the zero point. The term scale, as far as the interpretation I think you'd be most comfortable with in grade 10, is really the units in which the data are measured. (There are connections to other meanings of the word scale, which you don't have to worry about at your stage, so I won't get into them.)
I'll do one example with change in origin, one with change of scale, and one with change of both.
Suppose we are weighing items (say, gears of the same size) made in a factory. There is a common zero point: 0 kg (= 0 lb). We calculate that the mean of the gears is 10kg. We then learn that the the scale (the device we use to measure - isn't English fun?) is faulty, and it adds 2 kg to every weight. This means that the origin of the measurements has changed: under our measurements, it was 2 instead of zero. Instead of getting a new scale, and weighing all over again, we can subtract 2 from each measurement. Since we divide by the number of measurements, all we have to do is subtract 2 from the mean: our new mean is 8kg. (That is: (x1−2+⋯+xn−2)/n=x¯−2 .
Same situation as above. The factory's client prefers weighting in pounds. We could get a different scale that weighs in pounds are re-weight, we know that there are about 2.20462 lbs in a kg, and 8 kg is 17.637 lbs. (Again, we didn't even have to change each measurement, just the unit or scale of the average.) If we discovered the mistake in the scale and the preference for pounds at the same time, we have that 17.637 = (10-2) x 2.20462.
We've already done a change in location and scale in 2, but we'll do a different one. Suppose we have an accurate thermometer that measures in Fahrenheit and we'd like the mean to be in Celsius instead. Since C = (F -32) x 5/9, we could apply that formula to either all of the measurements, or, just the mean.
I hope that clears things up a little.
Answer:
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Step-by-step explanation:
Instead of getting a new scale, and weighing all over again, we can subtract 2 from each measurement. Since we divide by the number of measurements, all we have to do is subtract 2 from the mean: our new mean is 8kg. (That is: (x1−2+⋯+xn−2)/n=x¯−2(x1−2+⋯+xn−2)/n=x¯−2. Same situation as above.