Answer :
To find the first quartile, median, and third quartile values of the data set 275, 257, 301, 218, 265, 242, 201, follow these steps:
1. Sort the Data Set:
Arrange the numbers in ascending order:
[tex]\[
201, 218, 242, 257, 265, 275, 301
\][/tex]
2. Find the Median (Second Quartile):
The median is the middle number in the sorted list. Since there are 7 numbers, the median is the 4th number:
[tex]\[
\text{Median} = 257
\][/tex]
3. Find the First Quartile (Q1):
The first quartile is the median of the lower half of the data (not including the overall median if the number of data points is odd). The lower half of the data is 201, 218, 242. The median of this subset is:
[tex]\[
\text{First Quartile} = 218
\][/tex]
4. Find the Third Quartile (Q3):
The third quartile is the median of the upper half of the data (not including the overall median if the number of data points is odd). The upper half of the data is 265, 275, 301. The median of this subset is:
[tex]\[
\text{Third Quartile} = 275
\][/tex]
Based on these calculations, the final results are:
- First Quartile (Q1): 218
- Median: 257
- Third Quartile (Q3): 275
Thus, the correct selection from the given options is:
- First quartile = 218, median = 257, third quartile = 275
1. Sort the Data Set:
Arrange the numbers in ascending order:
[tex]\[
201, 218, 242, 257, 265, 275, 301
\][/tex]
2. Find the Median (Second Quartile):
The median is the middle number in the sorted list. Since there are 7 numbers, the median is the 4th number:
[tex]\[
\text{Median} = 257
\][/tex]
3. Find the First Quartile (Q1):
The first quartile is the median of the lower half of the data (not including the overall median if the number of data points is odd). The lower half of the data is 201, 218, 242. The median of this subset is:
[tex]\[
\text{First Quartile} = 218
\][/tex]
4. Find the Third Quartile (Q3):
The third quartile is the median of the upper half of the data (not including the overall median if the number of data points is odd). The upper half of the data is 265, 275, 301. The median of this subset is:
[tex]\[
\text{Third Quartile} = 275
\][/tex]
Based on these calculations, the final results are:
- First Quartile (Q1): 218
- Median: 257
- Third Quartile (Q3): 275
Thus, the correct selection from the given options is:
- First quartile = 218, median = 257, third quartile = 275
