Question

the table shows the number of insects that eight students on a science trip collected: Alan(14),Joann(16),Kris(9),Luis (15),JP(12),Mario(11)nick(10,Sheila(8) find the percentile rank for Alans number of insects and for Joannas number of insects

Answer 1

We have been given a table that shows number of insects collected by 8 students on a science trip.

Let us order our given data from least to greatest.  

Sheila (8), Kris (9), Nick (10), Mario (11), JP (12), Alan (14), Luis(15) and Joann (16).      

A. Let us find percentile rank for Alan's number of insects.

We will use percentile rank formula: $P=100\cdot\frac{(i-0.5)}{n}$, where i is rank of our data set, n is total number of our data sets.

We can see that Alan's data rank is 6 and total number of our data set is 8. Upon substituting our values in above formula we will get,  

$P=100\cdot\frac{(6-0.5)}{8}$

$P=100\cdot\frac{(5.5)}{8}$

$P=12.5\cdot 5.5$

$P=68.75\approx69$        

Therefore, percentile rank for Alan's number of insects is 68.75.

B. Let us find percentile rank for Joann's number of insects.

We can see that Joann's data rank is 8. Upon substituting our values in above formula we will get,

$P=100\cdot\frac{(8-0.5)}{8}$

$P=100\cdot\frac{(7.5)}{8}$

$P=12.5\cdot 7.5$

$P=93.75\approx94$

Therefore, percentile rank for Joann's number of insects is 93.75.