In a survey, two groups of students were asked whether they would prefer to be Happy, Rich, or Famous - Junior Cycle Mathematics - Question 4 - 2014

From the previous part, we know there were 90 students in the 12 – 15 age group. Therefore, there are also 90 students in the 16 – 19 age group.

• Happy: 50
• Rich: 25
• Famous: 15

We can fill in the missing bar:

$90 - (50 + 25) = 15$

Thus, 15 students from the 16 – 19 age group prefer to be Famous.

For the 12 – 15 year olds, the fraction who prefers to be Happy is:

$\frac{40}{90} = \frac{4}{9}$

For the 16 – 19 year olds, the fraction who prefers to be Happy is:

$\frac{50}{90} = \frac{5}{9}$

Therefore, the fractions are:

• 12 – 15 year olds: $\frac{4}{9}$
• 16 – 19 year olds: $\frac{5}{9}$

The pie chart does not represent the results of the 16 – 19 year olds, but rather the 12 – 15 year olds. This is because in the pie chart, the portion representing Happy is less than half of the total. The preference distribution for the 12 – 15 age group shows that Happy is less than half, justifying its representation in the pie chart.