Question

The test scores for 9 students on the Unit 1 Test were 35, 25, 50, 95, 80, 60, 45, 100, and 90.
What is the value of the third quartile for this data set?

answers below:

85

90

92.5

95

Answer 1

To find the third quartile (Q3) for the given data set, we first need to arrange the test scores in ascending order:

25, 35, 45, 50, 60, 80, 90, 95, 100

Next, we identify the position of the third quartile. The third quartile is the median of the upper half of the data.

Since there are 9 data points (an odd number), we first find the median (Q2):

1. The median position is given by the formula:
\[
\text{Median Position} = \frac{n + 1}{2} = \frac{9 + 1}{2} = 5
\]
The median is the 5th score in the ordered list, which is 60.

Now, we find the upper half of the data, which includes the scores above the median:

Upper half (after the median): 80, 90, 95, 100

To find the third quartile (Q3), we look at the median of this upper half:

1. The upper half consists of 4 values (80, 90, 95, 100). The median position for this subset is:
\[
\text{Q3 Median Position} = \frac{4 + 1}{2} = 2.5
\]
This means Q3 is the average of the 2nd and 3rd values in the upper half:

The 2nd value = 90
The 3rd value = 95

Thus, we calculate Q3:
\[
Q3 = \frac{90 + 95}{2} = \frac{185}{2} = 92.5
\]

Therefore, the third quartile (Q3) for this data set is **92.5**.