The average of a group of seven test scores is 80. If the lowest and highest scores are thrown out the average of the remaining scores is 78. What is the average of the lowest and highest scores?
If the lowest and highest are x and y, then we have, adding up all the points:
x+5*78+y = 80*7
x+y = 560-390 = 170
(x+y)/2 = 85
To find the average of the lowest and highest scores, we need to determine the sum of these scores and then divide it by 2 (since there are only two scores).
First, let's find the sum of the seven test scores. We know that the average of these scores is 80, so we can multiply 80 by 7 to get the sum:
Sum of the seven test scores = 80 * 7 = 560
Next, we need to find the sum of the remaining scores after removing the highest and lowest scores. We are given that the average of these scores is 78, so we can multiply 78 by 5 (since there are five remaining scores) to find the sum:
Sum of remaining scores = 78 * 5 = 390
Now, we can calculate the sum of the lowest and highest scores by subtracting the sum of the remaining scores from the sum of the seven test scores:
Sum of lowest and highest scores = Sum of the seven test scores - Sum of remaining scores
= 560 - 390
= 170
Finally, to find the average of the lowest and highest scores, we divide this sum by 2 (since there are two scores):
Average of lowest and highest scores = Sum of lowest and highest scores / 2
= 170 / 2
= 85
Therefore, the average of the lowest and highest scores is 85.