Question

The weights of seven frogs were studied. All the weights were muntiples of ten. The heaviest frog weighed 300 grams and the lightest weighed 100 grams. The media weight was 130 grams. The mean weight was 150 grams, and the mode weight was 110 grams. What is the only sequence of seven weights to fit this description?

Answer 1

The numbers given in the previous answer cannot right be because the mode would be 130 and 110, and the problem specifiies that the mode is 110.

This is how you can obtaind the numbers, step by step:

1) If the median is 130, there are 3 numbers less than 130 and 3 number over 130.

2) One of the numbers below 130 is 100 (the minimum reported), then the other two has to be 110 because 110 is the mode.

Now we have these numbers for sure 100, 110, 110 and 130 and 300.

3) We need to find only two more numbers, which are greater than 130 y less than 300.

4) Given the the mean is 150, the sum of all the numbers is 150*7 = 1050.

and the two so far unknown numbers add up : 1050 - 300 - 130 - 110 - 110 - 100 = 300.

5) The two numbers have to be different and greater than 130, then they are 140 and 160.

They cannot be 150 because they would be equal, they cannot be 170 and 130, because 130 is not the mode.

So you can be sure that the other two numbers are 140 and 160 and now we have the list of the seven numbers complete:

Answer: 100, 110, 110, 130, 140, 160 and 300 

 

Answer 2

The weights of the seven frogs divided by 7 gives 150. The weight we are given are: 300, 100, 130 and 110, which has the highest frequency.
To get the total number of weight, x: x/7= 150.
x =150 *7 = 1050.
300+100+130+110=640
1050 - 640=410.
410 - 110 - 130 = 170.
Thus, the last sequence for the description is 190.
The complete weights are:300, 170, 130, 130 110, 110, 100