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Please help me! use the following set of data: 20, 28, 30, 6, 15,18, 21, 22, 25, 29, 24, and 26. What are the third and first quartiles of the data?

User Melike
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Answer:

The first quartile (Q1) is 19, and the third quartile (Q3) is 28.5 for the given data set.

Explanation:

To find the first and third quartiles of the given data set, you first need to arrange the data in ascending order. Here's the sorted data set:

6, 15, 18, 20, 21, 22, 24, 25, 26, 28, 29, 30

The first quartile (Q1) represents the 25th percentile, and the third quartile (Q3) represents the 75th percentile of the data.

To find Q1:

Calculate the index (k) corresponding to the 25th percentile: k = (25/100) * (n + 1), where n is the number of data points.

If k is an integer, Q1 is the value at the kth position in the sorted data set.

If k is not an integer, round it up to the nearest whole number to get the position of the value (k_ceiling). Q1 will be the average of the values at positions k_ceiling and k_ceiling + 1.

To find Q3:

Calculate the index (k) corresponding to the 75th percentile: k = (75/100) * (n + 1).

If k is an integer, Q3 is the value at the kth position in the sorted data set.

If k is not an integer, round it up to the nearest whole number to get the position of the value (k_ceiling). Q3 will be the average of the values at positions k_ceiling and k_ceiling + 1.

Let's calculate Q1 and Q3:

Q1:

k = (25/100) * (12 + 1) = 3.25

k_ceiling = ceil(3.25) = 4

Q1 = (18 + 20) / 2 = 38 / 2 = 19

Q3:

k = (75/100) * (12 + 1) = 9.75

k_ceiling = ceil(9.75) = 10

Q3 = (28 + 29) / 2 = 57 / 2 = 28.5

So, the first quartile (Q1) is 19, and the third quartile (Q3) is 28.5 for the given data set.

User Charlie Davies
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