Find the value of the 90th percentile of the following set of data.
18, 9, 7, 5, 11, 7, 17, 20, 19, 2, 17, 12, 5, 1, 13, 12, 11, 15, 16, 20
To find the value of the 90th percentile, we first need to arrange the data in ascending order:
1, 2, 5, 5, 7, 7, 9, 11, 11, 12, 12, 13, 15, 16, 17, 17, 18, 19, 20, 20.
The 90th percentile is the value that is greater than or equal to 90% of the data values. Since we have 20 data values, the 90th percentile is the value at the 18th position.
Therefore, the value of the 90th percentile is 18. Answer: \boxed{18}.
are you sure
Apologies for the confusion. Let's proceed to find the correct value of the 90th percentile.
To find the value of the 90th percentile, we need to arrange the data in ascending order:
1, 2, 5, 5, 7, 7, 9, 11, 11, 12, 12, 13, 15, 16, 17, 17, 18, 19, 20, 20.
Since we have 20 data values, we need to find the position of the 90th percentile. The formula to calculate the position of a percentile is:
Position = (percentile/100) * (n + 1)
where n is the total number of data values. In this case, n = 20.
Plugging in the values, we get:
Position = (90/100) * (20 + 1)
Position = (0.90) * (21)
Position = 18.9
Since the position should be a whole number, we need to round up to the nearest whole number. Therefore, the position of the 90th percentile is 19.
To find the value at the 90th percentile, we look at the value at the 19th position in the ordered data. Crossing out values from the left, we get:
1, 2, 5, 5, 7, 7, 9, 11, 11, 12, 12, 13, 15, 16, 17, 17, 18, 19, 20, 20.
The value at the 19th position is 19.
Therefore, the value of the 90th percentile is 19. Answer: \boxed{19}.