Question - Statistical Quartiles Calculation
Solution:
The image shows a list of numbers: 31, 33, 35, 57, 80, 87. To find the lower quartile, median, and upper quartile, follow these steps:1. **Median:** Since there are 6 numbers, the median will be the average of the 3rd and 4th numbers, which are 35 and 57. \[ \text{Median} = \frac{35 + 57}{2} = \frac{92}{2} = 46 \]2. **Lower Quartile (Q1):** For an even set of numbers, the lower quartile is the median of the lower half of the data (not including the median if the data set count is odd). The lower half of the data set is 31, 33, 35. Since there are three numbers, the middle one is the median. Thus, the lower quartile is 33.3. **Upper Quartile (Q3):** Similarly for the upper quartile, which is the median of the upper half of the data, the upper half is 57, 80, 87. Again, because there are three numbers, the middle one is the median of this subset. So, the upper quartile is 80.Therefore, the lower quartile is 33, the median is 46, and the upper quartile is 80.
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