The mean of a data set of 12 p observations is 19.25.If one more value is included in the data then the new data with 13 observations,mean becomes 20?

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The mean of a data set of 12 p observations is 19.25.If one more value is included in the data then the new data with 13 observations,mean becomes 20?

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The mean of a data set of 12 p observations is 19.25.If one more value...

Let the total of first 12 observations be T and the 13th observation be X.

Then,

Mean of 12 observations = 19.25

=> T/n = 19.25

=> T/12 = 19.25

=> T = 19.25 * 12

=> T = 231 . . (i).

So,

New Total = T + 13th Observation = T + X.

And,

New Mean = 20

=> New Total / 13 = 20

=> (T+X) / 13 = 20

=> T + X = 20 * 13

=> 231 + X = 260 [Using Equation (i)]

=> X = 260 - 231

=> X = 29

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