The five-number summary provides five critical values from a dataset:
1. Minimum value (smallest value)
2. First quartile (Q1) – the value below which 25% of the data fall
3. Median (Q2) – the middle data point, which divides the data into two halves
4. Third quartile (Q3) – the value above which 25% of the data fall, or equivalently, below which 75% of the data fall
5. Maximum value (largest value)
In the given five-number summary, the values are:
1. Minimum: 18
2. Q1: 39
3. Median (Q2): 62
4. Q3: 76
5. Maximum: 100
The percentile of a value is the percent of observations that lie below that value. Thus, the 80th percentile will be a value such that 80% of the data points are at or to the left of it on the number line.
Since Q3 (76) is the point where 75% of the data is to its left, and the maximum (100) is the point where 100% of the data is to its left, the 80th percentile must be larger than Q3 and smaller than the maximum because 80% is greater than 75% but less than 100%.
This means that the 80th percentile should fall between Q3 and the maximum value:
e. The 80th percentile is between 76 and 100.
So the correct answer is:
e. The 80th percentile is between 76 and 100.
