Question

Identify the third quartile in the following dataset:
53.3, 46.9, 48.1, 49.7, 52.1, 47.5, 47.2, 45.5

Answer 1

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.