Question

use the accompanying radiation levels (in $\frac{w}{kg}$) for 50 different cell - phones. find the quartile $q_{3}$. 0.22 0.22 0.29 0.47 0.59 0.62 0.64 0.66 0.78 0.87 0.90 0.90 0.91 0.96 0.96 0.98 0.98 1.01 1.09 1.10 1.10 1.11 1.12 1.15 1.16 1.16 1.21 1.22 1.23 1.23 1.25 1.27 1.27 1.27 1.27 1.30 1.31 1.33 1.33 1.33 1.34 1.34 1.38 1.40 1.43 1.43 1.45 1.47 1.49 1.51 $q_{3}=square\frac{w}{kg}$ (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Arrange data in order

The data is already in ascending - order.

Step2: Calculate the position of $Q_3$

The formula for the position of the third - quartile $Q_3$ is $i = \frac{3(n + 1)}{4}$, where $n=50$. So, $i=\frac{3\times(50 + 1)}{4}=\frac{3\times51}{4}=38.25$.

Step3: Interpolate to find $Q_3$

The 38th value in the ordered data set is $1.33$ and the 39th value is $1.34$. Using interpolation, $Q_3=1.33+(1.34 - 1.33)\times(38.25 - 38)=1.33 + 0.01\times0.25=1.3325\approx1.33$.

Answer:

$1.33$