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State true or false.

If the mean of 10 observations is 15 and that of other 15 observations is 18, then the mean of all the 25 observations is 16.8.

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Detailed Solution

We have to check if the mean of 10 observations is 15 and that of other 15 observations is 18, then the mean of all the 25 observations is 16.8.
We know that,

mean = sum of all observations number of observations

.
It is given that the mean of 10 observations is 15.
Putting the values in the formula,

15 = Sum of observations 10 ⇒ Sum of Observations= 150

Similarly,

18 = Sum of observations 15 ⇒ Sum of Observations= 270

Thus,
Total sum of observations= 150+270.
=420
Total number of observations= 25.
Calculating the final mean,

= 42025 = 16.8

Thus, the given statement is true.
Therefore, option 1 is correct.

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