examine the given dataset: 45, 45, 50, 60, 75, 35, 50, 50, 60, 65, 70, 70, 55\ncompute for the median value…

examine the given dataset: 45, 45, 50, 60, 75, 35, 50, 50, 60, 65, 70, 70, 55\ncompute for the median value and interquartile range.\nuse the keypad to enter your answer in the box. more symbols can be found using the drop - down arrow at the top of the keypad.\nthe median value of the dataset is \nthe value of $q_1$ is while the value of $q_3$ is \nthe interquartile range of the dataset is

examine the given dataset: 45, 45, 50, 60, 75, 35, 50, 50, 60, 65, 70, 70, 55\ncompute for the median value and interquartile range.\nuse the keypad to enter your answer in the box. more symbols can be found using the drop - down arrow at the top of the keypad.\nthe median value of the dataset is \nthe value of $q_1$ is while the value of $q_3$ is \nthe interquartile range of the dataset is

Answer

Answer:

The median value of the dataset is 55. The value of $Q_1$ is 47.5 while the value of $Q_3$ is 65. The interquartile range of the dataset is 17.5.

Explanation:

Step1: Sort the dataset

35, 35, 45, 45, 50, 50, 50, 55, 60, 60, 65, 70, 70, 75

Step2: Find the median

There are 14 data - points. The median is the average of the 7th and 8th ordered values. $\frac{50 + 55}{2}=52.5$.

Step3: Find the lower half

The lower half is 35, 35, 45, 45, 50, 50, 50. The median of the lower half ($Q_1$) is the 4th value, which is 45. But for an even - numbered lower - half set, we take the average of the 3rd and 4th values: $\frac{45+50}{2}=47.5$.

Step4: Find the upper half

The upper half is 55, 60, 60, 65, 70, 70, 75. The median of the upper half ($Q_3$) is the 4th value of this half, which is 65.

Step5: Calculate the interquartile range

$IQR = Q_3−Q_1=65 - 47.5 = 17.5$.