Calculating the Interquartile Range (IQR) is a useful tool for understanding data sets. It helps us to understand the range of values within a given data set, which is particularly helpful when trying to better understand how to interpret data. The IQR is a measure of variation, and is calculated by finding the difference between the upper and lower quartiles of a data set. Knowing how to calculate IQR is important for anyone who works with data. In this blog post, we’ll explain in detail how to calculate IQR, and why it’s important to learn this valuable tool. We’ll also provide you with useful tips and tricks to help make IQR calculations easier and more efficient.
How to calculate IQR
Use the steps below to calculate the formula for IQR:
1. Arrange data in ascending order
List your data values in order from least to greatest. Determine the median once the values are arranged in ascending order. This value is the midpoint in your data set, which separates the upper 50% from the lower 50%
By counting the values to the left and right of the middle number to make sure each side has the same amount, you can quickly determine the median in an odd set of numbers. In the example set {4. 5, 6. 7, 6. 9, 7. 3, 10. 1}, 6. Because there are two values on either side of the median, it is 9.
2. Find the first quartile
Between the first point and the median point in the data, there is the first quartile. Use the median of the entire data set as the starting point for a new range that extends from the first data point to the median. The median value of this new range is in the first quartile.
Using the example test scores {83, 86. 5, 87, 88. 5, 89, 89. 5, 91, 95. 5, 98, 98. 5, 99. 5}, the median is 89. 5, making a new range between points 83 and 89. Find the median of the new range between 83 and 86 to determine the first quartile. 5, 87, 88. 5, 89}. 87 is the first quartile because it appears in the middle of this sample.
3. Calculate the third quartile
The third quartile represents the median of the upper 50% of a data set The third quartile is located between the median and the highest point in the data, much like the first quartile. Using the example scores {83, 86. 5, 87, 88. 5, 89, 89. 5, 91, 95. 5, 98, 98. 5, 99. 5}, create a new range between 91 and 99. 5, as these values are situated between the data’s endpoint and median point. The new range is {91, 95. 5, 98, 98. 5, 99. 5} and gives you 98 for the third quartile.
4. Subtract to find IQR
With the quartiles in hand, divide the first by the third. You can assess additional statistical metrics like standard deviation and variance using the interquartile range, which is the outcome. In the example test scores {83, 86. 5, 87, 88. 5, 89, 89. 5, 91, 95. 5, 98, 98. 5, 99. 5, 98 – 87 = 11, so the IQR is 11.
5. Calculate the median in even data sets
The median may not be as obvious when determining the interquartile range for a set of data with an even number of values. Take the mean of the two middle values in these situations to determine the median of your data. To determine the IQR, find the first and third quartiles and then subtract them. The two middle values in the example data set are 46 and 58 (numbers 22, 34, 42, 46, 58, 62, 64, and 74). You get a median of 52 by taking the average of these two values.
6. Use the median to find the first and third quartiles
The first and third quartiles can be determined using the preceding steps before calculating the median. The lower range contains the values 22, 34, 42, 46, and the upper range contains the values 58, 62, 64, 74 using the example data 22, 34, 42, 46, 58, 62, 64, and 52 as the median. Find the medians of each set using the mean of the two middle values because both ranges have an even number of values. The first quartile is now 38, and the third quartile is now 63.
7. Find the IQR
To calculate the IQR, subtract the first quartile from the third using the interquartile formula. Using the previous examples and the formula, this results in:
IQR = (63 – 38) = 25
This value can be used to locate outliers in the data set, or values that deviate greatly from the data’s mean.
What is the interquartile range in statistics?
The median spread of points in a set of data is represented by the interquartile range, which is a statistical measure of variance. It represents the middle 50% of data values and is an important statistical measurement that gives a more accurate perspective of the spread of a data set
The interquartile range, as opposed to the range, measures the spread of the data between the medians of the first and third quartiles. Because of this, the IQR is crucial for locating outliers in a data set. You can find the interquartile range using this formula:
IQR = (Q3) – (Q1)
What fields use IQR calculations?
The interquartile range can be used to estimate how widely dispersed data is from the mean of the values. The data points spread further from the mean when the IQR is high, while the data points cluster closer to the mean when the IQR is low. Therefore, calculating the IQR of a data set can be helpful for many purposes in various industries, such as:
Finance
The interquartile range frequently applies most to analysis in financial and accounting practices. Analyzing trends, risks, and return opportunities for investments like stocks and mutual funds requires the use of statistical data, such as averages and IQRs.
The use of statistical measures like mean, IQR, and variance in corporate accounting helps businesses make critical financial decisions. Financial institutions that provide credit and loans occasionally use IQR to comprehend average credit scores and the distribution of data around those average scores.
Health care and medicine
Clinical researchers measure data using a variety of metrics, and statistical research is a crucial tool in the pharmaceutical and healthcare industries. Professionals in these fields can benefit from the IQR’s ability to measure data spreads in medical research, treatment studies, and disease diagnosis. Many researchers use the interquartile range to examine the average outcomes from pharmaceutical and clinical trials because it considers mean data spread. Understanding outliers, deviation, and other variations is crucial in this regard.
Education
Interquartile range, quartile range, mean, and other statistical measures are used by academics to assess a variety of educational factors. IQR is frequently used in exams to generate standardized scores, which instructors can use to contrast student data. When creating academic standards and objectives, the education sector also uses IQR because these median ranges provide information on the typical success rates of instructional strategies. When teaching students about statistics and data analysis, math teachers also use the interquartile range.
Technology
In the technology sector, where experts rely on data analysis for many applications, statistics and data science are crucial. For instance, in software development, IQR measurement can be used to make decisions about usability, UX, and security implementations when calculating deviation and variance to code and evaluate program functionality. To comprehend how artificial networks respond to commands and produce outputs, machine learning also depends on statistical calculations, such as IQR.
Business
Additionally, statistical data like IQR, standard deviations, means, and variances are used in the business sector. In some cases, customer research, competitor analysis, and strategy integration in business and marketing analytics use IQR. The interquartile range is one of the statistics that can be used in the field of sales. Professionals in human resources management may rely on the information provided by IQRs to guide hiring, policy, and financial decisions for organizations.
Example of calculating IQR
Patients attempting a novel medication that lowers high blood pressure are having their diastolic blood pressure measured by a clinical researcher. With a sample size of 15, the researcher records that the median diastolic blood pressure was 72.
The lowest and highest seven values are placed on either side of 72 to determine the quartiles. This puts the values {65, 66, 67, 68, 69, 70, 71} in the lower 50% and {73, 74, 75, 76, 77, 78, 79} in the upper 50% The doctor calculates the IQR as (76 – 68 = 8) using the median values from both data sets.
This measure can assist the researcher in identifying any outliers in the sample. They multiply IQR x 1. 5 and add the third quartile to get 88. The clinician may encounter outliers on the high end of the data if any data points increase above this value. The researcher multiplies the IQR by one to determine whether there are any outliers on the lower end. 5 and gets 56 by taking this out of the first quartile. Therefore, any values that fall below this metric are also considered outliers.
How to Find the Interquartile Range of a Set of Data | Statistics
FAQ
How do you find Q3 with Q1 and Iqr?
- Lower Quartile (Q1) = (N+1) * 1 / 4.
- Middle Quartile (Q2) = (N+1) * 2 / 4.
- Upper Quartile (Q3 )= (N+1) * 3 / 4.
- Interquartile Range = Q3 – Q1.
How do you find Q1 Q2 and Q3?
- Lower quartile (Q1) formula: N 1 times (1) divided by (4).
- Middle quartile (Q2) formula is N 1 times (2) divided by (4).
- Upper quartile (Q3) formula is N 1 times (3) divided by (4).
