Statistical Analysis of Numerical Data
The image shows a set of numerical data: 31, 33, 35, 57, 80, 87. To find the lower quartile, median, and upper quartile of this data set, we need to follow these steps:
1. **Median**: Since there are 6 numbers, the median will be the average of the 3rd and 4th numbers. Therefore, the median is (35 + 57) / 2 = 92 / 2 = 46.
2. **Lower Quartile**: The lower quartile (Q1) is the median of the lower half of the data set (excluding the median if the number of observations is odd). With the data set split into two halves (31, 33, 35) and (57, 80, 87), the median of the lower half is 33, since it is the middle value of the first three numbers.
3. **Upper Quartile**: The upper quartile (Q3) is the median of the upper half of the data set (again excluding the median if the number of observations is odd). For the upper half (57, 80, 87), the median is 80, as it is the middle value of the last three numbers.
Thus, the lower quartile is 33, the median is 46, and the upper quartile is 80.
