The test scores for 9 students on the Unit 1 Test were 35, 25, 50, 95, 80, 60, 45, 100, and 90.

Question

What is the value of the first quartile for this data set?

answers below:

40

60

80

100

Answer 1

To find the first quartile (Q1) of the given data set, we first need to organize the test scores in ascending order. The test scores are:

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

Arranging them in ascending order gives us:

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

Once the data is ordered, we can determine the quartiles. The first quartile (Q1) is the median of the first half of the data.

1. The dataset has 9 numbers, so the median (Q2) will be the middle number, which is the 5th number in our ordered list.

   • The list is: 25, 35, 45, 50, 60, 80, 90, 95, 100.
   • The median (Q2) is 60.

2. The first half of the data (for Q1) consists of the first 4 numbers:

   • 25, 35, 45, 50.

3. To find Q1, we need the median of these four numbers. Since there are an even number of observations in this case (4), we take the average of the two middle numbers:

   • The two middle numbers are 35 and 45.
   • Average of 35 and 45 = (35 + 45) / 2 = 80 / 2 = 40.

Thus, the first quartile (Q1) is 40.

The correct answer is:

40.