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The interquartile range (IQR) can be calculated as:
IQR = Q3 – Q1
which is 160 – 60 = 100.
20 40 60 80 100 110 120 140 160 180 200
Q1 Q2 Q3
As reported on a weather report, the temperature ranges for the day are an important application of quartiles. If
there are irregularities, they may have a big impact on the range values. The top and bottom 25 percentiles of the
data points are thus preferred to be ignored in favour of the IQR. IQR is more resilient and a better reflection of the
degree of dispersion in the data when there are irregularities.
4.6. DECILES
Decile is a technique that is used to divide a distribution into ten equivalent parts. When data is divided into
deciles, a decile rank is allotted to each data point in order to sort the data into an ascending or descending order.
Each section of the sorted data denotes 1/10 of the original sample or population. This ordering is done with the
help of a scale from 1 to 10, where each successive value represents an increase of 10 percentage points. A decile
has 10 categorical buckets, a quartile has 4, and a percentile has 100.
In the fields of finance and economics, the concept of a decile is commonly used to analyse data. It can be used to
check the performance of a portfolio in the field of finance.
The higher the place in the decile ranking, the higher is the overall ranking. For example, a person getting 98
percentiles in an exam would be placed in a decile ranking of 10. But, a person receiving 5 percentiles in the same
exam would be placed in a decile ranking of 1.
The formula for calculating decile is:
(n + 1)
Di = i × 10 Data
th
Where:
th
i is the i decile and can be represented as:
(n + 1)
st
1 Decile, D = 1 × 10 data
th
1
(n + 1)
2 Decile, D = 2 × 10 data
nd
th
2
and so on
n is the number of data in the population sample.
Follow the given steps to calculate decile:
Step 1 Find the number of data or variables in the sample or population which is denoted by n.
Step 2 Now, arrange all the data or variables in the sample or population in ascending order.
Step 3 Then, based on the decile that is to be find, calculate the decile by using the formula:
(n + 1)
Di = i × 10 Data
th
Step 4 Finally, based on the decile value, find the corresponding variable from amongst the population data.
Let us take an example to understand the concept in detail:
Suppose we have 22 random numbers between 24 and 70. We want to represent them as deciles.
The numbers are:
[25, 33, 28, 45, 42, 36, 54, 68, 44, 35, 26, 37, 43, 55, 64, 65, 30, 39, 47, 52, 58, 66]
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