Find the minimum, first quartile, median, third quartile, and maximum of the data set below.
4.5 3.1 6 5.2 4.8 5.1 6.1 4.2 11.8
To calculate the minimum, first quartile (Q1), median, third quartile (Q3), and maximum from the given dataset, you must first arrange the data in ascending order. The dataset you've provided is:
4.5, 3.1, 6, 5.2, 4.8, 5.1, 6.1, 4.2, 11.8
Arranged in ascending order:
3.1, 4.2, 4.5, 4.8, 5.1, 5.2, 6, 6.1, 11.8
With the data ordered, we can find:
Minimum: The smallest number in the dataset, which is 3.1.
Maximum: The largest number in the dataset, which is 11.8.
Median: The median is the middle number when the data is ordered. Since we have 9 numbers (an odd number), the median will be the middle one, which is the fifth number in the sorted list:
3.1, 4.2, 4.5, 4.8, (5.1), 5.2, 6, 6.1, 11.8
So, the median is 5.1.
First Quartile (Q1): To find the first quartile, we take the median of the lower half of the data. Note that when finding Q1 and Q3, we do not include the overall median if the number of data points is odd.
Lower half (not including the median): 3.1, 4.2, 4.5, 4.8
The median of this half (Q1) is the average of the middle two values since we have an even number of values in this half:
(4.2 + 4.5) / 2 = 8.7 / 2 = 4.35
So, the first quartile Q1 is 4.35.
Third Quartile (Q3): To find the third quartile, we take the median of the upper half of the data (again, not including the median):
Upper half: 5.2, 6, 6.1, 11.8
The median of this half (Q3) is similarly found by averaging the middle two values:
(6 + 6.1) / 2 = 12.1 / 2 = 6.05
So, the third quartile Q3 is 6.05.
In summary:
- Minimum: 3.1
- First Quartile (Q1): 4.35
- Median: 5.1
- Third Quartile (Q3): 6.05
- Maximum: 11.8