   SEARCH HOME Math Central Quandaries & Queries  Question from farah, a student: the average height of a group of 25 students goes up by 2 cm when a student of height 165 cm replaces a student from the group. What is the height of the boy who went out of the group? Hi Farah.

We don't know the average height of the first group, but let's call it A. Since the average is the total height divided by the number of students, we know that the total of all the heights of the first group is A times 25.

We know that the average increases by two for the second group, which also has 25 people in it. So this group's average is two cm more: (A+2). That means the total of all the heights in the second group is (A+2) times 25.

Using this, you can find the difference between the total heights of the two groups, even if you don't know what A is.

We also know that the difference in the total heights of the two groups is just the difference in the heights of the two students (the one who left and the 165cm one who replaced her). So the difference between the total heights of the two groups is the same as the difference in heights of the two people.

Hope this helps,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.