Question

the data below give the age of a random sample of 18 student calculate the percentile rank of 48 and the 32 round solution to one decimal place

Answer 1

Let's use the formula

$\frac{x+0.5y}{n}\cdot100$

In the first case of 48, we have x = 14, y = 4, and n = 18.

$\frac{14+0.5\cdot4}{18}\cdot100=\frac{14+2}{18}\cdot100=\frac{16}{18}\cdot100=88.9$

The percentile rank of 48 is 88.9%.

Now, let's apply the same process for 32. In this case, x = 6, y = 1, and n = 18. Let's use the formula

$\frac{x+0.5y}{n}\cdot100=\frac{6+0.5\cdot1}{18}\cdot100=\frac{6.5}{18}\cdot100=36.1$

The percentile rank of 32 is 36.1%.

Remember that x represents the number of students below the value, y represents the frequency of the value and n represents the total number of students.