5.2 Measures of Relative Standing
5.2: Measures of Relative Standing
5.2.1: Measures of Relative Standing
Measures of relative standing can be used to compare values from different data sets, or to compare values within the same data set.
Learning Objective
Outline how percentiles and quartiles measure relative standing within a data set.
Key Takeaways
Key Points
- The common measures of relative standing or location are quartiles and percentiles.
- A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall.
- The 25th percentile is also known as the first quartile (Q1), the 50th percentile as the median or second quartile (Q2), and the 75th percentile as the third quartile (Q3).
- To calculate quartiles and percentiles, the data must be ordered from smallest to largest.
- For very large populations following a normal distribution, percentiles may often be represented by reference to a normal curve plot.
- Percentiles represent the area under the normal curve, increasing from left to right.
Key Terms
- percentile
- any of the ninety-nine points that divide an ordered distribution into one hundred parts, each containing one per cent of the population
- quartile
- any of the three points that divide an ordered distribution into four parts, each containing a quarter of the population
Example
For runners in a race, a low time means a faster run. The winners in a race have the shortest running times. Is it more desirable to have a finish time with a high or a low percentile when running a race? b. The 20th percentile of run times in a particular race is 5.2 minutes. Write a sentence interpreting the 20th percentile in the context of the situation. c. A bicyclist in the 90th percentile of a bicycle race between two towns completed the race in 1 hour and 12 minutes. Is he among the fastest or slowest cyclists in the race? Write a sentence interpreting the 90th percentile in the context of the situation. SOLUTION a. For runners in a race it is more desirable to have a low percentile for finish time. A low percentile means a short time, which is faster. b. INTERPRETATION: 20% of runners finished the race in 5.2 minutes or less. 80% of runners finished the race in 5.2 minutes or longer. c. He is among the slowest cyclists (90% of cyclists were faster than him. ) INTERPRETATION: 90% of cyclists had a finish time of 1 hour, 12 minutes or less.Only 10% of cyclists had a finish time of 1 hour, 12 minutes or longer.
Measures of relative standing, in the statistical sense, can be defined as measures that can be used to compare values from different data sets, or to compare values within the same data set.
Quartiles and Percentiles
The common measures of relative standing or location are quartiles and percentiles. A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall. For example, the 20th