Consider the following dataset: 22, 29, 31, 30, 22, 24, 18, 20, 25. What is the third quartile’s value? Round to the nearest tenth if necessary.(1 point)
To find the third quartile's value, you first need to arrange the dataset in ascending order:
18, 20, 22, 22, 24, 25, 29, 30, 31
The third quartile divides the dataset into two halves, with 75% of the data below it and 25% above it. In this case, we have 9 data points, so the third quartile falls at the position (9+1) * 0.75 = 7.5, which is between the 7th and 8th values.
The 7th value is 29 and the 8th value is 30. To find the value between them, you can take the average of the two values:
(29 + 30) / 2 = 59 / 2 = 29.5
Therefore, the third quartile's value is 29.5.
To find the third quartile's value, we need to first arrange the dataset in ascending order: 18, 20, 22, 22, 24, 25, 29, 30, 31.
Since there are 9 numbers in the dataset, the third quartile is the number that splits the upper half of the dataset into two equal parts, which falls on the 75th percentile.
To find the index of the number that represents the 75th percentile, we use the formula: index = (n + 1) * P / 100.
In this case, index = (9 + 1) * 75 / 100 = 10 * 0.75 = 7.5.
Since the index is a non-integer value, we need to take the average of the numbers at the 7th and 8th positions in the dataset: (25 + 29) / 2 = 54 / 2 = 27.
Therefore, the third quartile's value is 27.
wrong
Apologies for the incorrect response. Let's recalculate the third quartile using the correct methodology.
To find the third quartile, we need to first arrange the dataset in ascending order: 18, 20, 22, 22, 24, 25, 29, 30, 31.
Since there are 9 numbers in the dataset, the third quartile is the number that splits the upper half of the dataset into two equal parts, which falls on the 75th percentile.
To find the index of the number that represents the 75th percentile, we use the formula: index = (n + 1) * P / 100.
In this case, index = (9 + 1) * 75 / 100 = 10 * 0.75 = 7.5.
Since the index is a non-integer value, we need to take the average of the numbers at the 7th and 8th positions in the dataset: (25 + 29) / 2 = 54 / 2 = 27.
Therefore, the third quartile's value is 27.
Given the following dataset, what are the extremes?
58, 32, 8, 25, 13, 12, 3, 11, 22, 10(1 point)
The smallest extreme value is
.
The largest extreme value is
.
To find the third quartile's value, we need to first arrange the dataset in ascending order.
18, 20, 22, 22, 24, 25, 29, 30, 31
Next, we need to determine the position of the third quartile in the dataset. The formula to calculate the position of a quartile is as follows:
Position = (n + 1) * (Q / 4)
Where n is the number of data points and Q is the desired quartile. In this case, the third quartile is Q = 3.
n = 9, Q = 3
Position = (9 + 1) * (3 / 4)
Position = 10 * (3 / 4)
Position = 7.5
Since the position is not a whole number, we take the average of the values at the 7th and 8th positions:
Value at the 7th position: 25
Value at the 8th position: 29
(25 + 29) / 2 = 27
Therefore, the third quartile's value is 27.