To find the quartiles in the data set 55, 55, 59, 60, 62, 65, 64, we first need to arrange the numbers in ascending order.
After sorting the data, we have: 55, 55, 59, 60, 62, 64, 65.
The quartiles divide the data into four equal parts. To find them, follow these steps:
- First Quartile (Q1): This is the median of the first half of the data (the lower half). For our sorted data, the lower half is 55, 55, 59. The median here is the middle number, which is 55.
- Second Quartile (Q2): This is simply the median of the entire data set. Since there are 7 numbers, the median is the 4th number in the sorted list, which is 60.
- Third Quartile (Q3): This is the median of the upper half of the data. The upper half is 62, 64, 65. The median here is the middle number, which is 64.
In summary, the quartiles for our data set are:
- Q1 = 55
- Q2 = 60
- Q3 = 64