To find the quartiles for the set of numbers, we first need to organize the data in ascending order. The given numbers are:
86, 72, 61, 91, 93, 97, 77, 85, 74, 75, 74
Arranging these in order gives us:
61, 72, 74, 74, 75, 77, 85, 86, 91, 93, 97
Now we can determine the minimum and various quartiles:
Minimum: The smallest number in the sorted list is 61.
Next, we will determine the quartiles:
-
First Quartile (Q1) - This is the median of the first half of the data (the 1st quartile separates the lowest 25% of data).
- The numbers in the first half are: 61, 72, 74, 74, 75
- The median of this subset (the 3rd number in a sorted 5 number sequence) is 74.
-
Second Quartile (Q2 or Median) - This is the median of the entire sorted data set.
- There are 11 numbers total, so the median will be the 6th number: 77.
-
Third Quartile (Q3) - This is the median of the second half of the data (the 3rd quartile separates the lowest 75% of data).
- The numbers in the second half are: 77, 85, 86, 91, 93, 97
- The median of this subset (the 3rd number in a sorted 6 number sequence) is 91.
To summarize:
- Minimum = 61
- Q1 = 74
- Q2 (Median) = 77
- Q3 = 91
So, the answer to your question about the minimum is: 61.