Identify the third quartile in the following dataset:

53.3, 46.9, 48.1, 49.7, 52.1, 47.5, 47.2, 45.5(1 point)
Responses

53.3
53.3

50.9
50.9

47.05
47.05

47.8

1 answer

To find the third quartile (Q3) of the given dataset, we first need to arrange the numbers in ascending order and then calculate the quartiles.

The given dataset is: 53.3, 46.9, 48.1, 49.7, 52.1, 47.5, 47.2, 45.5

Arranging the numbers in ascending order: 45.5, 46.9, 47.2, 47.5, 48.1, 49.7, 52.1, 53.3

Now, we have 8 data points. To find the quartiles:

  • The median (Q2) will be the average of the 4th and 5th values: Q2 = (47.5 + 48.1) / 2 = 47.8

For the third quartile (Q3), which is the median of the upper half of the dataset (the values above the median), we take:

  • The upper half: 48.1, 49.7, 52.1, 53.3
  • The median of this upper half (Q3) will be the average of the 2nd and 3rd values: Q3 = (49.7 + 52.1) / 2 = 50.9

Thus, the third quartile (Q3) of the dataset is 50.9.

So, the correct response is: 50.9