The median is the middle value. The quartiles are three values that divide a data set into four equally large parts.
Minimum: 46.4 First Quartile: 48.5 Median: 50.4 Third Quartile: 52.5 Maximum: 55.9
Practice makes perfect
We want to find the five number summary, which includes minimum, first quartile, median, third quartile, and maximum of the given data set.
Median
Notice that the given data is already arranged in numerical order. When this is the case, the median is the middle value — or the mean of the two middle values — in a set of data. Let's find the median of the given data set.
46.4, 46.9, 47.7, 48.1, 48.5, 48.5, 48.8, 49.0, 49.3, 50.0, 50.1, 50.4,
50.6, 51.1, 51.4, 51.8, 52.4, 52.5, 53.2, 53.8, 54.4, 55.1, 55.9The median of this set is 50.4.
Minimum and Maximum
The minimum and the maximum are the least and the greatest values in a set of data. For our exercise, the least value is 46.4 and the greatest value is 55.9.
Minimum:& 46.4
Maximum:& 55.9
Quartiles
To find the quartiles, let's recall their definitions.
The First Quartile (Q1) is the median of the lower half of the data set.
The Third Quartile (Q3): is the median of the upper half of the data set.
Since our values are already written in numerical order, let's find the first and the third quartile.
46.4, 46.9, 47.7, 48.1, 48.5, 48.5, 48.8, 49.0, 49.3, 50.0, 50.1, 50.4,
50.6, 51.1, 51.4, 51.8, 52.4, 52.5, 53.2, 53.8, 54.4, 55.1, 55.9
We found that the first quartile of the given data set is 48.5 and the third quartile is 52.5.
