Quartile search algorithm:
Quartiles are calculated using the median. If the number of records is an even number, i.e. 2n, then the first quartile (Q1) is equal to the median of n smallest records, and the third quartile (Q3) is equal to the median of n largest records.
If the number of records is odd, that is, in the form (2n + 1), then
- the first quartile (Q1) is the median of n smallest records
- third quartile (Q1) is the median of n largest records
- second quartile (Q2) is the same, like a normal median.
Range: is the difference between the largest value and the smallest value in a given dataset.
Interquartile range:
Interquartile range (IQR), also called mean or mean 50% , or technically H-spread — it is the difference between the third quartile (Q3) and the first quartile (Q1). It covers the distribution center and contains 50% of the observations. IQR = Q3 — Q1
Uses :
- The interquartile range has a breakdown point of 25%, which is why it is often preferred over the entire range.
- IQR is used to plot box plots, simple graphical representations of probability distributions.
- IQR can also be used to identify outliers in a given dataset.
- IQR gives the central trend of the data .
Make a decision
- The dataset has a higher interquartile range (IQR) and more variability.
- A dataset with a lower interquartile range (IQR) is preferred.
Suppose that if we have two datasets and their interquartile ranges are IR1 and IR2, and if IR1 & gt; IR2, it is said that the data in IR1 has more variability than the data in IR2, and the data in IR2 is preferable.
Example :
- Below is the number of candidates enrolled each day in the last 20 days for the course —
Data Structures and Algorithms — DSA Online 3 in Python.Engineering
75, 69, 56, 46, 47, 79, 92, 97, 89, 88, 36, 96, 105, 32, 116, 101, 79, 93, 91, 112
- After sorting the above dataset:
32, 36, 46, 47, 56, 69, 75, 79, 79, 88, 89, 91, 92, 93, 96, 97, 101, 105, 112, 116
- The total number of terms here is 20.
- The second quartile (Q2) or median of the above data is (88 + 89) / 2 = 88.5
- First quartile (Q1) is the median of the first n, that is, 10 terms (or n, that is, 10 smallest values) = 62.5
- Third quartile (Q3) — this is the median n, i.e. The 10 largest values (or the last n, i.e. 10 values) = 96.5.
- Then IQR = Q3 — Q1 = 96.5 — 62.5 = 34.0
Interquartile range using numpy.median
|
import numpy as np
data = [ 32 , 36 , 46 , 47 , 56 , 69 , 75 , 79 , 79 , 88 , 89 , 91 , 92 , 93 , 96 , 97 ,
101 , 105 , 112 , 116 ]
Q1 = np.median (data [: 10 ])
Q3 = np.median (data [ 10 :])
IQR = Q3 - Q1
print (IQR)
|
Output: 34.0
Interquartile range using numpy.percentile
|
import numpy as np
data = [ 32 , 36 , 46 , 47 , 56 , 69 , 75 , 79 , 79 , 88 , 89 , 91 , 92 , 93 < / code> , 96 , 97 ,
101 , 105 , 112 , 116 ]
Q1 = np.percentile (data, 25 , interpolation = `midpoint` )
Q3 = np.percentile (data, 75 , interpolation = ` midpoint` )
IQR = Q3 - Q1
print (IQR)
|
Output: 34.0 Interquartile range using scipy.stats.iqr
| from scipy import stats data = [ 32 , 36 , 46 , 47 , 56 , 69 , 75 , 79 , 79 , 88 , 89 , 91 , 92 , 93 , 96 , 97 , 101 , 105 , 112 , 116 ]
IQR = stats.iqr (data, interpolation = ` midpoint` ) print (IQR) |
Output: 34.0
< strong> Quartile Deviation
Quartile Deviation — this is half the difference between the third quartile (Q3) and the first quartile (Q1), i.e. half of the interquartile range (IQR). (Q3 — Q1) / 2 = IQR / 2
Make a decision
Dataset with higher quartile deviation , has higher volatility.
Quartile deflection using numpy.median
|
import numpy as np
data = [ 32 , 36 , 46 , 47 , 56 , 69 , 75 , 79 , 79 , 88 , 89 , 91 , 92 , 93 , 96 , 97 ,
101 , 105 , 112 , 116 ]
Q1 = np.median (data [: 10 ])
Q3 = np.median (data [ 10 :])
IQR = Q3 - Q1
qd = IQR / 2
print (qd)
|
Output: 17.0
