Statistics » Mean with variables

At some of the exercises the mean of all the pupils is given, but they want to know the number of pupils of one of the two groups.

Example 1
The mean of two vwo 4 classes is a 7.5.
The mean of V4a is a 7.9 and the mean of V4b is a 6.9.
In V4b there are 24 pupils.
How many pupils are in V4a?

Answer:
To calculate the number of pupils V4a you can use the total number of points of the classes together and the separate classes.
The unknown value, the number of pupils in V4a, will be the variable x.

V4a has a total of 7.9x points. The mean times the number of pupils.
The total of V4b is 6.9 × 24 = 165.6 points.
Together, the two classes have 7.5(24 + x) points.
Again, this is the mean times the number of pupils, which is (24 + x).

number of points in V4a + number of points in V4b = total number of points.

We can make and solve an equation using the formulas we just made:

7.9x + 165.6	= 7.5(24 + x)
7.9x + 165.6	= 180 + 7.5x
7.9x	= 14.4 + 7.5x
0.4x	= 14.4x
x	= 36

There are 36 pupils in V4a.

In other exercises, the mean is given, but the question is about how the group is composed.

Example 2
The mean of a class with 30 pupils is 7.4.
The boys in this class had a mean of 7.0.
The girls in this class had a mean of 8.0.
How many girls are in this class?

Answer
To calculate the number of girls in this class we can use the total number of points for the class, the boys an the girls.
The unknown value, the number of girls, will be the variable x.

The girls have a total of 8.0x points. The mean times the number of girls.
The boys have a total of 7.0(30 – x) points. The mean times the number of boys, which is the other half of the class (30 – x).
The total number of points for the class is 7.4 × 30 = 222.

points of the boys + points of the girls = total number of points.

We can make and solve an equation using the formulas we just made:

7.0(30 – x) + 8.0x	= 222
210 – 7.0x + 8.0x	= 222
210 + 1.0x	= 222
x	= 12

The number of girls in this class is 12.