Finding Quartiles of a Dataset
To solve the question, we need to find the lower quartile, median, and upper quartile of the given data set. Let's first arrange the data in order:
14, 20, 31, 38, 45, 54, 81, 87, 92
From the image, it's clear that the data is already sorted in ascending order. There are nine numbers in the series, so the median (the middle value) will be the fifth number:
Median = 45
The lower quartile (Q1) is the median of the lower half of the data, excluding the median of the entire set if the size is an odd number, so we look at the first four numbers:
14, 20, 31, 38
The median of these four numbers is the average of the middle two values:
Lower quartile (Q1) = (20 + 31) / 2 = 51 / 2 = 25.5
The upper quartile (Q3) is the median of the upper half of the data, excluding the median of the entire set. We consider the last four numbers:
54, 81, 87, 92
The median of these four numbers is the average of the middle two values:
Upper quartile (Q3) = (81 + 87) / 2 = 168 / 2 = 84
So, the lower quartile is 25.5, the median is 45, and the upper quartile is 84.
