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

Question

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, median, and third quartile, we'll follow these steps:

1. Order the data set: The data set provided is: 275, 257, 301, 218, 265, 242, 201.
   When we sort this in ascending order, we have:
   201, 218, 242, 257, 265, 275, 301.

2. Find the median: The median is the middle value of the ordered data set.
   Since there are 7 numbers (an odd count), the median is the fourth number:
   Median = 257.

3. Calculate the first quartile (Q1): The first quartile is the median of the lower half of the data. The lower half (excluding the median) is:
   201, 218, 242.
   The median of these three numbers is:
   Q1 = 218.

4. Calculate the third quartile (Q3): The third quartile is the median of the upper half of the data. The upper half (excluding the median) is:
   265, 275, 301.
   The median of these three numbers is:
   Q3 = 275.

So, we find:

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

The correct answer is: first quartile = 218, median = 257, third quartile = 275.