What is the lowest number, greatest number, 1st quartile, 2nd quartile, 3rd quartile, and 4th quartile of the data set:
39, 41, 33, 57, 34, 30, 47, 33, 49, 52, 32, 53, 37, 43
First, we need to sort the data set in ascending order:
30, 32, 33, 33, 34, 37, 39, 41, 43, 47, 49, 52, 53, 57
Now find the different values:
- The lowest number: 30
- The greatest number: 57
- The 1st quartile (Q1) is the median of the first half of the data set. Since there are 14 numbers (an even number), the first half consists of the first 7 numbers: 30, 32, 33, 33, 34, 37, 39. The median of this set is the middle number: 33.
- The 2nd quartile (Q2) is the median of the entire data set. The middle of the data set is between 37 and 41, so the median is the average of these two numbers: (37 + 41) / 2 = 39.
- The 3rd quartile (Q3) is the median of the second half of the data set. The second half consists of the last 7 numbers: 43, 47, 49, 52, 53, 57. The median of this set is the middle number: 49.
- There is no 4th quartile, as the term is typically only used for 3 quartiles (Q1, Q2, and Q3).
So, the values are:
- Lowest number: 30
- Greatest number: 57
- 1st quartile: 33
- 2nd quartile: 39
- 3rd quartile: 49