Statıstıcs I Deneme Sınavı Sorusu #817457
What happens to arithmetic average of a data set if all observations are increased by 4?
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It doesn't change. |
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It increases by 4. |
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It decreases by 4. |
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It increases by 2. |
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It decreases by 2. |
Yanıt Açıklaması:
Suppose there are n observations; x1, x2, x3, x4.......xn, and the arithmetic mean is k. Thus the sum of observations is n*k=(x1+x2+x3+x4.......+xn). If we increase all observations by 4, the new values will be 4+x1, 4+x2, 4+x3, 4+x4.......4+xn. Thus the new sum will be (4+4+...+4)+(x1+x2+x3+x4.......+xn)=4n+nk=n(4+k). If we divide this sum by n then the new arithmetic mean will be 4+k.
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