Final answer:
The combined arithmetic mean is 6. Therefore, the answer is option (C) 6.
Step-by-step explanation:
To find the combined arithmetic mean, we need to consider both sets of items. Let's call the first set of 10 items Set A and the second set of 5 items Set B.
The arithmetic mean of Set A is 4, which means the sum of all the items in Set A is 4 times 10. Similarly, the arithmetic mean of Set B is 10, which means the sum of all the items in Set B is 10 times 5.
To find the combined arithmetic mean, we need to add the two sums together and divide by the total number of items. So, the combined arithmetic mean is: [(4 times 10) + (10 times 5)] / (10 + 5).
To find the combined arithmetic mean of the two sets of items, we can use the formula for the weighted mean given that there are different numbers of items in each set. The mean for 10 items is 4, and for 5 items is 10. To combine these, we find the total sum of values for each set and then divide by the total number of items.
The sum for the first set is 10 items × 4 = 40.
Simplifying this expression gives us a combined arithmetic mean of 6. Therefore, the answer is option (C) 6.