Video Transcript
Noah took samples of students from each grade in his school to investigate the
average height of a student. The results are summarized as shown. Use his data to find the mean height of a student in the school. Give your answer to the nearest centimeter.
Let’s look more closely at the data Noah has collected. In each grade from kindergarten to grade five, Noah has sampled a number of students,
which is given in the second row of the table, and calculated the mean height for
that group of students, which is given in the bottom row of the table. We need to use this data to find the mean height of a student in the school across
all grades.
We recall that the mean of a data set is found by calculating the sum of all the
values in the data set and dividing this by how many values there are. To find the mean height of a student in the school then, Noah needs to find the total
height of all the students in his sample and divide this by the total number of
students in the sample. We can find the total number of students in the sample by summing the values in the
second row of the table, 14 plus 16 plus 15 plus 19 plus 17 plus 18, which is
99.
To find the total height of all the students, we first need to find the total or
combined height of all the students in each grade. We can do this by recalling that within each grade, the mean height for that grade
will have been calculated by dividing the combined height of all students who were
sampled in that grade by how many students in that grade were sampled. So, for example, in grade K, the combined height of the students divided by 14 gives
the mean height of 116 centimeters. We can then work out the combined height of all the students sampled from grade K by
multiplying both sides of this equation by 14. This gives 1,624, and the units for this are centimeters.
We can add an extra row to the table to record the combined height of the students
sampled in each grade. For grade K, we’ve already worked this out. And for each of the remaining grades, we calculate this by multiplying the number of
students by the mean height for that grade. We then find the total height of all students across all grades by summing these six
values, giving 12,892 centimeters.
The mean height of the students across all grades is then equal to this total divided
by the total number of students sampled, which was 99. This is equal to 130.2 recurring, or 130 to the nearest integer.
By first finding the total height within each grade and then using this to calculate
the overall total height, we’ve found that the mean height of a student in Noah’s
school is 130 centimeters.
