Cumulative Percent and Percentile Rank

Fundamentals of Social Statistics by Adam J. McKee

A cumulative percentage indicates the percentage of scores at and below a given score.  A cumulative percentage is also known as a percentile rank.  Most college student is familiar with percentile ranks because they have been given their percentile rank on standardized college admission tests.  If you scored in the 87th Percentile on the SAT, that means that 87% of the students taking the test when you did had the same or a lower score than you did.

Cumulative percentages, or percentile ranks, offer a valuable tool in understanding the relative standing of an observation or score within a given data set. These percentiles have widespread use, not just in educational settings like SAT scores but also extensively in the realm of social sciences, especially in criminal justice.

Cumulative Percentage in Criminal Justice

Use in Recidivism Studies

One of the pressing concerns in criminal justice is recidivism, which refers to a person’s relapse into criminal behavior. Researchers may utilize cumulative percentages to determine how a particular individual’s risk of reoffending compares to a broader population. For instance, if an individual’s risk factor is at the 70th percentile, it suggests that their risk is higher than 70% of the studied population. Such information can be instrumental in formulating post-release programs or interventions tailored to individuals’ risk levels.

Evaluating Police Performance

Cumulative percentages are also invaluable when assessing police departments’ performance across different jurisdictions. For example, if a particular precinct’s response time to emergencies is at the 90th percentile, it indicates a higher efficiency compared to 90% of other precincts. Such statistics can be instrumental for policymakers when allocating resources, setting training priorities, or implementing changes in strategy.

Application in Other Social Sciences

Social Mobility Studies

Social mobility, the ability of individuals or families to move up or down the social and economic ladder, often uses percentile ranks for analysis. If a study finds that an individual born in a low-income household rises to the 80th percentile of income distribution, it sheds light on the structural opportunities and barriers in society. Such insights are essential for formulating policies to ensure equitable chances for all citizens.

Assessing Mental Health in Populations

Cumulative percentages play a pivotal role in mental health research. For instance, in studying the prevalence of certain psychological disorders, researchers might find that an individual’s symptom severity is in the 95th percentile, implying a severity higher than 95% of the population. Such data can guide healthcare professionals in diagnosing, formulating treatment plans, and managing patient care.

Quartiles as Special Percentiles

In statistics, quartiles hold a unique position as they divide data into four equal parts, each representing a specific portion of the population. In social sciences, understanding quartiles can be instrumental in grasping the distribution of a particular trait or characteristic within a population.

Crime Rates and Quartiles

Take, for instance, the analysis of crime rates in different cities. If City A’s burglary rate falls in the Third Quartile (or 75th Percentile), it suggests that this city has a higher burglary rate than 75% of cities in the study. Such a distinction allows city administrators and law enforcement to understand their relative position and strategize accordingly.

Income Distribution and Social Equality

Income distribution often uses quartiles to understand wealth distribution within a country or region. If a significant portion of a nation’s wealth is concentrated in the Fourth Quartile, it indicates wealth disparity, which can be a focal point for policymakers aiming to create more egalitarian societies.

Computing Cumulative Percentages

Understanding the computation of cumulative percentages or percentiles is essential for anyone dealing with extensive sets of data. The process can be undertaken manually or with the aid of software tools such as Excel, offering a streamlined approach, especially for larger datasets. Here’s a breakdown of both techniques:

Manual Calculation of Cumulative Percentages

  1. Ordering the Data: Begin by arranging the data in ascending order, transitioning from the smallest to the most significant value.
  2. Determining Position: To identify the percentile of a specific value, employ the following formula: P = (r/n) x 100 Where P stands for the percentile, r signifies the rank of the value, and n denotes the total number of values.
  3. Quartiles:
    • First Quartile (Q1): Represents the 25th percentile. The formula is: Q1 = (n+1)/4
    • Second Quartile (Q2 or Median): Denotes the 50th percentile. Q2 = (n+1)/2
    • Third Quartile (Q3): Symbolizes the 75th percentile. Q3 = 3(n+1)/4

Using Excel to Compute Cumulative Percentages

  • Sorting the Data: Commence by sorting your data range in ascending order using Excel’s SORT function or the sorting tool.
  • Percentile Function: Implement the ‘PERCENTILE’ function in Excel to ascertain the percentile for a specific value. The formula’s structure is: =PERCENTILE(array, k) Where ‘array’ is your data’s range, and ‘k’ is the desired percentile in decimal form (e.g., 0.25 for the 25th percentile).


  • First Quartile (Q1): Apply the formula: =QUARTILE(array, 1)
  • Second Quartile (Q2): =QUARTILE(array, 2)
  • Third Quartile (Q3): =QUARTILE(array, 3)

While calculating percentiles manually can offer a foundational understanding of the mechanics, tools like Excel significantly simplify the procedure, particularly for expansive data sets. Irrespective of the method selected, grasping the fundamental principles to interpret and utilize the outcomes effectively remains crucial.


Cumulative percentages, or percentiles, are powerful statistical tools that provide a relative perspective on data, making them invaluable in fields like criminal justice and broader social sciences. Whether it’s understanding crime rates, gauging social mobility, or assessing mental health prevalence, percentiles offer nuanced insights that can guide research, policy-making, and intervention strategies. The use of quartiles, a specific type of percentile, further aids in breaking down data into comprehensible segments, allowing for a clearer analysis and understanding.


Cumulative percentages, commonly known as percentile ranks, offer a way to understand the relative position of a score within a dataset. Familiar to most through standardized testing scores, they have broader applications in fields like criminal justice and other social sciences. In the criminal justice domain, they assist in evaluating risks such as recidivism and assessing police performance. In other social sciences, they play roles in analyzing social mobility and mental health trends. Quartiles, dividing data into four equal parts, are specialized percentiles used for further nuanced insights, as seen in analyses of crime rates or income distributions. The process of calculating these percentiles can be manually executed or streamlined using tools like Excel. Regardless of the chosen method, understanding the underlying principles and the implications of these percentiles is crucial in research, policy decisions, and intervention designs.

Key Terms

Percentage, Proportion, Rate, Cumulative Percent, Percentile Rank

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Last Modified:  09/25/2023

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