# Interquartile Range Formula

## Interquartile Range Formula

In addition to being a less sensitive indicator of the data’s distribution, the Interquartile Range Formula is crucial. The Interquartile Range Formula is used to determine when a number is an outlier since it is resistant to outliers. It explains how to distribute all the information. Students can determine the strength of the outlier they have by looking at the interquartile range. They should either look below the first quartile or above the third quartile when searching for an outlier. The interquartile range numbers determine how far they should go. Due to the fact that the interquartile range is less susceptible to outliers than the range, it is frequently used to assess the spread of data instead of the range. A measure of variability based on splitting a data set into quartiles is called the Interquartile Range Formula (IQR). The first, second, and third quartiles—abbreviated Q1, Q2, and Q3, respectively—are the values that separate each portion.

Q1 is the “middle” value in the first half of the rank-ordered data set.

Q2 is the set’s median value.

Q3 is the “middle” number in the rank-ordered data set’s second half.

## What is Interquartile Range Formula?

The quarter splits the data series into four equally sized segments. First Quartile, Second Quartile, Third Quartile, and Fourth Quartile are the four components of the quartile. Since it splits the data into equal portions, the second quartile is frequently referred to as the data series’ median.

• First Quartile

It splits the data into four equal halves, with 25% of the results falling below the first quartile and the remaining 75% falling above. The lower quartile is another name for the first quartile. It has the identifier Q1.

• Second Quartile

In order for 50% of the observations to be below the second quartile and another 50% to be above, the data are split into two equal halves. The second quartile is sometimes known as the median.

• Third Quartile

It splits the data into four equal halves, with three-fourths of the observations—or 75% of them—lying below the third quartile and one-fourth of the observations—or 25% of them—lying above it. The upper quartile is another name for the third quartile. It is designated as Q3.

The Interquartile Range Formula can be used to determine the difference between the third and first quartiles. The  Interquartile Range Formula calculates variability by splitting a collection of ordered data into quartiles. Quartiles are three values or cuts that split each component into the first, second, and third quartiles, represented by Q 1, Q 2, and Q 3.

The first-half cut of the rank-ordered data set is Q 1.

The set’s median value is Q 2.

The cut in the rank-ordered data set’s second half is Q 3.

### IQR Formula

The Interquartile Range Formula calculates the middle half of a data collection. The Interquartile Range is the least dispersed statistical metric. The interquartile range is the difference between the upper and lower quartiles.

The Interquartile Range Formula = Upper Quartile – Lower Quartile

IQR(Q2)=Q3–Q1

where,

IQR = Interquartile range (IQR = Q2)

Q1= (1/4)[(n + 1)]th term)

Q3 = (3/4)[(n + 1)]th term)

n = number of data points

### Solved Examples Using Interquartile Range Formula

Statistics is a branch of Mathematics concerned with data gathering, examination, and analysis. It is well-known for obtaining data inferences using quantified models. Statistical analysis is the process of gathering and analysing data before summarising it mathematically. The study of Statistics is the acquisition, analysis, interpretation, presentation, and organisation of data. In layman’s terms, it is a mathematical instrument used to collect and summarise data. Only statistical analysis can reveal uncertainty and fluctuation in many sectors and factors. The likelihood, which is particularly essential in statistics, determines these uncertainties.

Statistics, as students are aware, deals with information obtained for certain purposes. In the Interquartile Range Formula, students will learn about some of the most important measures of dispersion, as well as how to compute them for both ungrouped and grouped data. Students will learn about measures of dispersion, range, mean deviation, variance, standard deviation, and analysis of frequency distributions with identical means but differing variances in this chapter. By including Interquartile Range Formula as well as solved examples. It will either give conceptual knowledge or strengthen the basic component. Students can have a better knowledge of the content provided in the chapter by completing the three tasks and additional activities in the chapter. Students can study the Interquartile Range Formula from the Extramarks website or mobile application. The Interquartile Range Formula can also help them comprehend advanced statistical concepts.

Students who peruse the reference materials available on the Extramarks educational website can enhance their study abilities and accomplish their goals. These solved examples are deliberately chosen to help students learn and comprehend the Interquartile Range Formula. The language is simple enough for students to learn more and get the most out of their experience.

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