Read the mini lesson doc and/or watch the lesson video in the Message Board on quartile values then answer the following question.

Question

Using the data set 275, 257, 301, 218, 265, 242, 201

What are the first quartile, median, and third quartile values?

(1 point)
Responses

first quartile = 275, median = 218, third quartile = 201
first quartile = 275, median = 218, third quartile = 201

first quartile = 218, median = 257, third quartile = 275
first quartile = 218, median = 257, third quartile = 275

first quartile = 257, median = 218, third quartile = 242
first quartile = 257, median = 218, third quartile = 242

first quartile = 201, median = 257, third quartile = 301

Answer 1

To find the first quartile (Q1), median (Q2), and third quartile (Q3) for the given data set (275, 257, 301, 218, 265, 242, 201), we first need to sort the data in ascending order:

Sorted Data: 201, 218, 242, 257, 265, 275, 301

Now we can calculate the quartiles:

1. Median (Q2): The median is the middle value of the sorted data. Since there are 7 values in the sorted data set, the middle one is the 4th value.

   • Median = 257

2. First Quartile (Q1): The first quartile is the median of the first half of the data. The first half consists of the first 3 numbers: 201, 218, 242. The median of this subset (3 values) is the second value.

   • Q1 = 218

3. Third Quartile (Q3): The third quartile is the median of the second half of the data. The second half consists of the last 3 numbers: 265, 275, 301. The median of this subset (3 values) is the second value.

   • Q3 = 275

Thus, we have:

• First Quartile (Q1) = 218
• Median (Q2) = 257
• Third Quartile (Q3) = 275

The results are: first quartile = 218, median = 257, third quartile = 275.