Question

2. What is the value of the 30th percentile for the data set?7 12 3 14 17 20 5 3 17 4 13 2 15 9 15 18 16 9 1 69156

Answer 1

To calculate the percentile, we first rearrange the set of data

We have 20 numbers in the set

Thus we have,

1,2,3,3,4,5,6,7,9,9,12,13,14,15,15,16,17,17,18,20

The formula to calculate percentile is given by,

`\begin{gathered} P_x=(x)/(100)*(N+1)th \\ \text{where x is the percentile} \\ N\text{ is the number of data in the set} \end{gathered}`
`\begin{gathered} P_(30)=(30)/(100)*\text{ (20+1)} \\ P_(30)=(30)/(100)*21 \\ P_(30)=6.3_{} \end{gathered}`

This means the 30th percentile is the 6.3th term

So from the set of data, the 6.3th term will fall immediately after the 6th term

The 6th term in the rearranged data is 5.

Therefore the 6.3 th term is 6. So the 30th percentile for the data is 6