Statistical Data Analysis
This exercise is about finding the lower quartile, median, and upper quartile of the given set of numbers. The given dataset is already arranged in ascending order: 31, 33, 35, 57, 80, 87.
To find the median (which is also the second quartile), we find the middle value of the dataset. Since there are an even number of data points (6 numbers), the median will be the average of the two middle numbers (35 and 57).
Median = (35 + 57) / 2 = 92 / 2 = 46
Now, to find the lower quartile (first quartile), we take the median of the lower half of the dataset. The lower half (before the median value) is 31, 33, 35. Since there are three numbers, the middle one is the lower quartile.
Lower quartile = 33
To find the upper quartile (third quartile), we take the median of the upper half of the dataset. The upper half (after the median value) is 57, 80, 87. Since there are three numbers here as well, the middle one is the upper quartile.
Upper quartile = 80
Therefore, the lower quartile is 33, the median is 46, and the upper quartile is 80.
