Use the following data set to answer this question:
14, 17, 13, 15, 14, 19, 2, 18
What is the upper quartile?
*
15
15.5
17
17.5
To find the upper quartile, we need to first find the median and then find the median of the upper half of the data set.
First, let's arrange the data set in ascending order: 2, 13, 14, 14, 15, 17, 18, 19.
The median is the middle value of the data set, which is 15.
Next, we need to find the median of the upper half of the data set. The upper half is: 17, 18, 19.
The median of the upper half is (18 + 19) / 2 = 37 / 2 = 18.5.
Therefore, the upper quartile is 18.5.
To find the upper quartile, you first need to arrange the data set in ascending order:
2, 13, 14, 14, 15, 17, 18, 19
Since there are 8 data points in total, we need to find the median of the upper half of the data set. The upper half of the data set is:
15, 17, 18, 19
To find the median of this subset, we take the average of the two middle values. The two middle values are 17 and 18. Calculating the average of these two values gives us:
(17 + 18) / 2 = 35 / 2 = 17.5
Therefore, the upper quartile is 17.5.
To find the upper quartile, you first need to arrange the data set in ascending order:
2, 13, 14, 14, 15, 17, 18, 19
The upper quartile divides the data into the upper 25% of values. Since there are 8 values in the data set, you need to find the value that is at the 75th percentile.
You can calculate the position of the upper quartile using the formula:
Position = (75/100) * (n + 1)
where n is the number of values in the data set.
Plugging in the numbers, we have:
Position = (75/100) * (8 + 1)
Position = (3/4) * 9
Position = 6.75
Since the position is not a whole number, we need to take the average of the values at positions 6 and 7 to find the upper quartile.
So, the upper quartile is the average of the 6th and 7th values in the data set:
Upper quartile = (15 + 17) / 2
Upper quartile = 32 / 2
Upper quartile = 16
Therefore, the upper quartile of the given data set (14, 17, 13, 15, 14, 19, 2, 18) is 16.