Question

the accompanying radiation levels \\( \ln \frac { w } { \mathrm { kg } } \\) for 50 different cell phones. find the centile \\( p _ { 10 } \\)
\\( = \square \frac { \mathrm { w } } { \mathrm { kg } } \\) (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Calculate the position

Use the formula \(L = \frac{n\times p}{100}\), where \(n = 50\) (number of data points) and \(p = 10\) (percentile). So \(L=\frac{50\times10}{100}=5\).

Step2: Find the value

Since \(L = 5\) is an integer, the \(10^{th}\) percentile \(P_{10}\) is the average of the \(5^{th}\) and \(6^{th}\) ordered data values. Ordering the data (already ordered in the list), the \(5^{th}\) value is \(0.59\) and the \(6^{th}\) value is \(0.60\). Then \(P_{10}=\frac{0.59 + 0.60}{2}\).

Answer:

\(0.60\)