There are 10 observations x1, x2, x3, ....., x10 in a data. The first five elements x1, x2, ....., x5 are placed by x1 + 5, x2 + 5, ....., x5 + 5 respectively. Also, the next five elements x6, x7, ....., x10 are placed by x6 - 5, x7 - 5, ..., x10 - 5 respectively. Calculate the overall change in the mean of the data.

Question

KnowledgeBoat · Accepted Answer

Total observations = 10

First 5 numbers increased by 5

∴ Total increase in sum = 5 × 5 = 25

Next 5 numbers decreased by 5

∴ Total decrease in sum = 5 × 5 = 25

So, net change = 25 - 25 = 0

So new total sum = original total sum.

Hence, there is no change in the mean of a data.

Mathematics

Statistics

Answer

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