Week 4: Organizing and Displyain Data & Percentiles
KIN 610 - Spring 2023
Credits
(furtado2022?); Navarro and Foxcroft (2022)
Percentile and Percentile Rank
Percentiles and percentile rank are related concepts, but they have slightly different meanings.
A percentile is a specific value that indicates the percentage of values that are equal to or below a given value in a dataset. For example, the 75th percentile is the value below which 75% of the values in a dataset fall.
Percentile rank, on the other hand, is a measure of the relative position of a score within a distribution of scores. It indicates the percentage of scores that are equal to or below a given score. For example, if a score has a percentile rank of 75, it means that 75% of the scores in the distribution are equal to or below that score.
In essence, percentile rank uses percentiles to determine the relative position of a score within a dataset. While percentiles focus on specific values in a dataset, percentile rank focuses on the relative position of a score within the distribution of scores.
Intro to Percentiles
Definition of Percentiles
- A measure used in statistics
- Indicates the value below which a certain percentage of observations in a group fall
Example: 20th Percentile
- The value below which 20% of the observations may be found
- Can be used to compare the relative standing of a value within a dataset (Percentile Rank)
Example: 90th Percentile
- If a student’s test score is in the 90th percentile, it means that the student scored higher than 90% of the other students who took the test
Determining Distribution
- Percentiles can be used to determine the distribution of values within a dataset
- If the majority of scores fall within the lower percentiles, it may indicate that the scores are generally lower
- If the majority of scores fall within the higher percentiles, it may indicate that the scores are generally higher
Calculating Percentiles
In a nutshell…
- Percentiles can be calculated using a variety of methods
- One common method is to first arrange the data in order from smallest to largest
- Then identify the value that corresponds to the desired percentile
Doing it by hand
- Arrange the data set in numerical order
- Determine the position of the percentile you want to calculate in the data set
- E.g. 50th percentile is also known as the median
- Calculate the percentile by multiplying the position of the percentile by the total number of values in the data set and then dividing that number by 100
- E.g. (5 * 10) / 100 = 0.5 for the 50th percentile of a data set with 10 values
- To find the value at the percentile you calculated, go to the position in the data set that corresponds to the percentile value
Example 1:
- Data set: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- Find 50th percentile (median)
- Position: 50th percentile = (50 / 100) * 10 = 5
- Value: 5
Example 2:
- Data set: {5, 7, 8, 12, 14, 15, 16, 17, 18, 20}
- Find 75th percentile
- Position: 75th percentile = (75 / 100) * 10 = 7.5
- Value: average of 7th and 8th values = (16 + 17) / 2 = 16.5
Uses of Percentiles
Understanding the distribution of data
- Percentile can be used to understand the distribution of data.
- It indicates the value below which a certain percentage of data falls.
- For example, if the 50th percentile of a dataset is 50, it means that 50% of the data falls below that value.
Interpreting percentile values
Example 1: If the 10th percentile is 20 and the 90th percentile is 80, it means that 10% of the data falls below 20 and 90% of the data falls below 80.
- This indicates that the data is distributed relatively evenly, with a few outliers on either side.
Example 2: If the 10th percentile is 20 and the 90th percentile is 90, it means that there is a larger concentration of data towards the higher end of the scale.
Using percentile to understand data
- Using percentile can help us understand the distribution of data and identify patterns or trends in the data.
- It can also be used to compare different datasets and see how they differ in terms of distribution.
Comparing Data Sets
- Comparing data sets can be useful to understand how a particular value in one data set compares to values in another data set.
- Percentiles can be used for comparing data sets, especially when they have different scales or units of measurement.
Percentile rank
Definition of Percentile Rank
- Percentile rank is a measure of the relative standing of a value in a dataset
- Indicates the percentage of values in the dataset that are equal to or less than the value in question
- Example: if a value has a percentile rank of 75, it means that 75% of the values in the dataset are equal to or less than that value.
Application of Percentile Rank
- Percentile ranks are commonly used to describe how well a person has performed on a test or assessment relative to a group of people
- Example: a person scores in the 75th percentile on a test, it means that they scored higher than 75% of the people who took the test
- Percentile ranks can also be used to compare the scores of different groups of people, such as comparing the scores of students in different schools or at different grade levels.
Difference between Percentile Rank and Percentage
- It’s important to note that percentile rank is different from percentage
- Percentile rank describes the relative standing of a value within a dataset
- Percentage is a measure of the number of items in a set relative to the total number of items.
How to Calculate Percentile Rank
- Organize the scores in ascending order.
- The lowest score should be at the bottom.
- Identify the position of the score in the ordered distribution.
Calculate the percentile rank as a percentage.
- Divide the position of the score by the total number of scores.
- Multiply the result by 100 to get the percentile rank as a percentage.
Example: Let’s say we have the following distribution of scores: 60, 70, 75, 80, 85, 90, 95, 100. The percentile rank for a score of 80 would be:
- Organize the scores in ascending order: 60, 70, 75, 80, 85, 90, 95, 100.
- Determine the position of the score in question: The score of 80 is the 4th score in the distribution.
- Calculate the percentile rank as a percentage: 4/8 * 100 = 50%. The score of 80 is at the 50th percentile.
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