Question

QUESTION 2 Find the range for the given sample data. Jeanne is currently taking college economics. The instructor often gives quizzes. On the past five quizzes, Jeanne got the following scores: 6 20 1 15 10 Compute the range. O 1 020 O 19 1 p QUESTION 3 Find the percentile for the data point. Data set: 2 3 7425 10 9 11 3 3 10 6 1 10; data point 7 0 70 35

Answer 1

Solution :

Given that,

2 ) Range

= maximum(x_i) - minimum(x_i)

= 20 - 1

= 19

Range = 19

Answer 19 is correct.

3 )Percentile
Arrange the data in ascending order:
1, 2, 2, 3, 3, 3, 4, 5, 6, 7, 9, 10, 10, 10, 11
Compute the position of the pth percentile (index i):
i = (p / 100) * n),
where p = 7 and n = 15
i = (7 / 100) * 15
= 1.05
The 7^th percentile is the value in 2th position, or 2
Let's say we want to determine the 80th percentile for the following values:
10, 55, 50, 80, 85, 90, 20, 40, 55, 65, 30, 25.

Arrange the values from lowest to highest: 10, 20, 25, 30, 40, 50, 55, 55, 65, 80, 85, 90.

Calculate index i (the position of the pth percentile):

i = (p / 100) * n = 80 / 100 * 12 = 9.6

In this case, i is not an integer. As such, you should round up. The point of the 80th percentile is the next integer above 9.6, which is the 10^th position.
The 80^th percentile is the data value that appears in the 10^th position in the list of values: 80.

Let's look at a second example. This time, we want to calculate the 50^th percentile for the set of data.

Having arranged the values in ascending order, we have: 10, 55, 50, 80, 85, 90, 20, 40, 55, 65, 30, 25.

Calculate index i (the position of the p^th percentile):

i = (p / 100) * n = 50 / 100 * 12 = 6

In this case, i is an integer. As such, the 50^th percentile is the average of the values that appear in the 6^th and 7^th positions in the set of ordered data: 50 and 55 respectively.

Therefore, the 50^th percentile of this data set is (50 + 55) / 2 = 52.5.

Answer 52 to is correct.