The arithmetic mean of 12 observations is7.5.If the arithmetic mean of 7 of these observations is 6.5,the mean of remaining observations is?
The arithmetic mean of 12 observations is7.5.If the arithmetic mean of 7 of these observations is 6.5,the mean of remaining observations is?
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Mean of remaining observations is 8.9.
Step-by-step explanation:
We are given that the arithmetic mean of 12 observations is 7.5. The arithmetic mean of 7 of these observations is 6.5 and we have to find the mean of remaining observations.
Now, the mean of any data is given by the following formula;
Or
So, the arithmetic mean of 12 observations is given as 7.5, i.e;
where, = Sum of all 12 observations
7.5 =
So, = 90.
Now, also the arithmetic mean of 7 of these observations is 6.5;
Mean of 7 observations =
6.5 =
where, = Sum of 7 of these observations
So, = 45.5.
Now, the sum of remaining 5 observations is , that is;
=
= 90 - 45.5 = 44.5
Hence, the mean of remaining 5 observations =
= = 8.9
Therefore, the mean of remaining observations is 8.9.