Question

use the given sample data to find q3. 49 52 52 52 74 67 55 55 a. 55.0 b. 61.0 c. 6.0 d. 67.0

Explanation:

Step1: Sort the data

$49,52,52,52,55,55,67,74$

Step2: Calculate the position of $Q_3$

There are $n = 8$ data - points. The position of $Q_3$ is given by $i=\frac{3(n + 1)}{4}=\frac{3\times(8 + 1)}{4}=\frac{3\times9}{4}=6.75$.

Step3: Interpolate to find $Q_3$

The 6th value is $55$ and the 7th value is $67$. Using linear interpolation: $Q_3=55+(67 - 55)\times0.75=55 + 9=64$. However, if we use the method of not interpolating for simple cases (taking the value at the next - integer position when $i$ is not an integer), the 7th value in the sorted data set is $67$.

Answer:

D. 67.0