Given:
We're given a list of distances traveled to the workplace by 15 employees of a certain hospital.
To find:
We need to find 25 and 70 percentile of the given data.
Step-by-step solution:
We will firstly arrange the given data in ascending format:
5,6,7,9,11,13,14,15,18,18,20,31,34,36,37
We will now calculate the value of the 25th percentile:
L = k/100 × n
n = number of values = 15
k = percentile in question = 25
L = 25/100 × 15
L = 3.75
In case L is not an integer, The kth percentile is Lth value, where L has been rounded to next integer.
Thus 4th value is equal to 25th percentile.
The 25th percentile = 9 miles
We will now calculate the value of the 70th percentile:
L = k/100 × n
n = number of values = 15
k = percentile in question = 70
L = 70/100 × 15
L = 10.5
In case L is not an integer, The kth percentile is Lth value, where L has been rounded to the next integer.
Thus 11th value is equal to 70th percentile.
The 70th percentile = 20 miles
Final answer:
The 25th percentile = 9 miles
The 70th percentile = 20 miles