Question

A set of seven observations has mean ten and another set of three observations has mean five. The mean of the combined set is:
A. 15
B. 10
C. 8.5
D. 7.5

Answer 1

Hint: First of all, determine the sum of the 7 operations and then determine the sum of the 3 operations. After that determine the sum of both the operation 7 and 3. There are 10 total numbers of operations. And then divide the sum of both the operations by the total number of operations. Hence, we will get a suitable answer.

Complete step by step solution:
Let us assume that x and y are the sum of 7 and 3 operations respectively. And we have given that the mean of 7 operations are 10 and the mean of the 3 operations are the 5. Therefore,
We know that if the ${a_1}, {a_2}, {a_3}$ and ${a_n}$ are the integers, then the mean of these numbers is given by,
${ \Rightarrow mean} = {\dfrac{{{a_1} + {a_2} + {a_3}.... + {a_n}}}{n}} $
Now we have the mean of the 7 operations, therefore, we can write.
$ \Rightarrow {10} = {\dfrac{x}{7}} $
$ \Rightarrow x = {70} $
Similarly, for the 3 operations,
$ \Rightarrow y = {15} $
Now the total sum of these operations are,
$ \Rightarrow 70 + 15$
$ \Rightarrow 85$
Therefore the mean of the combined set is ,
$ \Rightarrow \dfrac{{85}}{{10}}$
$ \Rightarrow 8.5$
Now the final answer is 8.5.

Option ‘C’ is correct

Note: Remember that the total sum of the operation is calculated by adding the sum of the 7 and the sum of the 3 operations. The total number of operations is 10. So, to determine the mean of the total number of the operations, we will have to divide the total sum of both the operations by the total number of operations.