# The sum of the weights of 8 children is 520 pounds. No two children have the same weight. What is the average(mean) weight of he fourth and fifth heaviest children if the mean and median

## since you do not in fact specify anything about the mean and median, there are many possible answers.

Some possible set of weights are arithmetic sequences:
2, 20, 38, ..., 128
...
51, 53, 55, ..., 65

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## To find the average weight of the fourth and fifth heaviest children, we first need to determine the median weight.

Since there are 8 children, the median will be the value of the weight in the middle when arranged in ascending order.

Given that no two children have the same weight, the median weight will be the weight of the 4th child.

To find the average weight of the fourth and fifth heaviest children, we need to find the weights of these two children.

Let's assume the weights of the 8 children (in pounds) are as follows: w1, w2, w3, w4, w5, w6, w7, and w8.

Given that the sum of the weights of the 8 children is 520 pounds, we can write the equation:

w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 = 520

Now, since the median weight is the weight of the 4th child, we have:

w4 = median

To find the weights of the fourth and fifth heaviest children, we need to consider the remaining weights.

The sum of the weights of the remaining 6 children (w1, w2, w3, w6, w7, and w8) will be:

w1 + w2 + w3 + w6 + w7 + w8 = 520 - w4

Now, let's arrange these remaining weights in descending order:

w1 ≥ w2 ≥ w3 ≥ w6 ≥ w7 ≥ w8

Since the weights are all different, we know that w3 is the weight of the fifth heaviest child.

Therefore, the average weight of the fourth and fifth heaviest children can be calculated as:

Average weight = (w4 + w3) / 2

To find the values of w4 and w3, we will need more information.

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## To find the average weight of the fourth and fifth heaviest children, we first need to determine the total weight of all the children and the median weight.

Given that the sum of the weights of 8 children is 520 pounds, we can establish the total weight as 520 pounds.

To find the median weight, we need to arrange the weights of the children in ascending order. Since no two children have the same weight, we know that the median will be the weight of the child in the middle position when the weights are ordered.

Now, let's calculate the median:

1. Arrange the weights in ascending order.
2. Since there are 8 children, the weight in the middle position will be the 4th child.
3. If the weights were listed as (w1, w2, w3, w4, w5, w6, w7, w8), then the median weight would be w4.

Once we have the median weight, we can figure out the average weight of the fourth and fifth heaviest children.

1. Add up the weights of the 4th and 5th children.
2. Divide the sum of their weights by 2 (since we are finding the average of two numbers).

This will give us the average weight of the fourth and fifth heaviest children.

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