Question

use the accompanying radiation levels (in \\( \frac { w } { k g } \\) ) for 50 different cell phones. find the quartile \\( q _ { 3 } \\).
\\( q _ { 3 } = \square \frac { w } { k g } \\) (type an integer or decimal rounded to two decimal places as needed)

Explanation:

Step1: Arrange the data in ascending order

The data is already in ascending order (as per the given list).

Step2: Calculate the position of \(Q_3\)

The formula for the position of \(Q_3\) (third - quartile) is \(i=\frac{3(n + 1)}{4}\), where \(n = 50\) (number of data points).

$$i=\frac{3(50+ 1)}{4}=\frac{3\times51}{4}=38.25$$

Step3: Use the position formula for non - integer \(i\)

If \(i\) is not an integer, \(Q_3=x_{j}+(x_{j + 1}-x_{j})\times f\), where \(j\) is the integer part of \(i\) and \(f\) is the fractional part of \(i\). Here, \(j = 38\) and \(f=0.25\).
Counting the data points (the first row has 10 data points, the second row has 10, the third row has 10, the fourth row has 10, and the fifth row has 10).
The 38th data point \(x_{38}=1.30\) and the 39th data point \(x_{39}=1.30\)

$$Q_3=1.30+(1.30 - 1.30)\times0.25$$

Answer:

\(1.30\)