The mean of 15 observations is 32. Find the resulting mean, if each observation is :
(i) increased by 3
(ii) decreased by 7
(iii) multiplied by 2
(iv) divided by 0.5
(v) increased by 60%
(vi) decreased by 20%

Question

The mean of 15 observations is 32. Find the resulting mean, if each observation is :
(i) increased by 3
(ii) decreased by 7
(iii) multiplied by 2
(iv) divided by 0.5
(v) increased by 60%
(vi) decreased by 20%

KnowledgeBoat · Accepted Answer

(i) According to property 2, if each observation is increased by quantity `a`, then the mean is also increased by the same quantity `a`. The mean of 15 observations is 32. If each observation is increased by 3, then the mean increases by 3 ( 32 + 3 = 35). Hence, the mean of the new observations = 35. (ii) According to property 3, if each observation is decreased by a quantity `a`, then the mean is also decreased by the same quantity `a`. The mean of 15 observations is 32. If each observation is decreased by 7, then the mean is decreased by 7 ( 32 - 7 = 25). Hence, the mean of the new observations = 25. (iii) According to property 4, if each observation is multiplied by a quantity `a`, then the mean is also multiplied by the same quantity `a`. The mean of 15 observations is 32. If each observation is multiplied by 2, then the mean is multiplied by 2 ( 32 x 2 = 64). Hence, the mean of the new observations = 64. (iv) According to property 5, if each observation is divided by a quantity `a`, then the mean is also divided by the same quantity `a`. The mean of 15 observations is 32. If each observation of the data is divided by 0.5, then the mean is divided by 0.5 . Hence, the mean of the new observations = 64. (v) According to property 2, if each observation is increased by a quantity `a`, then the mean is also increased by the same quantity `a`. The mean of 15 observations is 32. If each observation is increased by 60%, then the mean is increased by 60% ( 32 + = 32 + 19.2 = 51.2). Hence, the mean of the new observations = 51.2. (vi) According to property 3, if each observation is decreased by a quantity `a`, then the mean is also decreased by the same quantity `a`. The mean of 15 observations is 32. If each observation is decreased by 20%; then the mean is decreased by 20% ( 32 - = 32 - 6.4 = 25.6). Hence, the mean of the new observations = 25.6.

Mathematics

The mean of 15 observations is 32. Find the resulting mean, if each observation is :
(i) increased by 3
(ii) decreased by 7
(iii) multiplied by 2
(iv) divided by 0.5
(v) increased by 60%
(vi) decreased by 20%

Statistics

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Mathematics

The mean of 15 observations is 32. Find the resulting mean, if each observation is :(i) increased by 3(ii) decreased by 7(iii) multiplied by 2(iv) divided by 0.5(v) increased by 60%(vi) decreased by 20%

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The mean of 15 observations is 32. Find the resulting mean, if each observation is :
(i) increased by 3
(ii) decreased by 7
(iii) multiplied by 2
(iv) divided by 0.5
(v) increased by 60%
(vi) decreased by 20%