Identify the third quartile in the following dataset:
53.3, 46.9, 48.1, 49.7, 52.1, 47.5, 47.2, 45.5
The third quartile (Q3) is the value separating the upper 25% of the dataset from the lower 75%.
To find the third quartile in this dataset, we first need to arrange the numbers in order from smallest to largest:
45.5, 46.9, 47.2, 47.5, 48.1, 49.7, 52.1, 53.3
There are a few ways to find Q3, but one common method is to first find the median (Q2), which is the value separating the lower 50% of the dataset from the upper 50%.
To find the median, we need to find the middle value in the dataset. Since there are 8 numbers, the middle is between the 4th and 5th numbers. So we take the average of those two numbers:
Median (Q2) = (47.5 + 48.1)/2 = 47.8
Now we can find Q3, which is the median of the upper half of the dataset (i.e. the four numbers greater than Q2).
Upper half: 49.7, 52.1, 53.3
Q3 = median of upper half
Q3 = (52.1 + 53.3)/2 = 52.7
Therefore, the third quartile in this dataset is 52.7.
To find the third quartile in a dataset, you need to determine the value below which 75% of the data falls.
First, arrange the dataset in ascending order:
45.5, 46.9, 47.2, 47.5, 48.1, 49.7, 52.1, 53.3
Next, calculate the index of the third quartile. Since 75% of the data falls below the third quartile, the index will be located at 75% of the total number of data points:
Index = (75 / 100) * (total number of data points)
Index = (75 / 100) * (8)
Index = 0.75 * 8
Index = 6
Finally, find the value at the index of the third quartile in the ordered dataset. The value at index 6 is 52.1.
Therefore, the third quartile in the given dataset is 52.1.