Interquartile Range And Quartile Deviation of One Array using SciPy
- We import NumPy and SciPy libraries.
- We define a sample dataset named
data. - We use SciPy’s
iqrfunction to directly calculate the interquartile range (IQR) of the dataset. - We then calculate the quartile deviation by dividing the IQR by 2.
Python3
import numpy as npfrom scipy.stats import iqr# Sample datasetdata = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])# Calculate Interquartile Range (IQR) using scipyiqr_value = iqr(data)# Calculate Quartile Deviationquartile_deviation = iqr_value / 2print("Interquartile Range (IQR):", iqr_value)print("Quartile Deviation:", quartile_deviation) |
Output:
Interquartile Range (IQR): 4.5
Quartile Deviation: 2.25
Interquartile Range and Quartile Deviation using NumPy and SciPy
In statistical analysis, understanding the spread or variability of a dataset is crucial for gaining insights into its distribution and characteristics. Two common measures used for quantifying this variability are the interquartile range (IQR) and quartile deviation.
Quartiles
Quartiles are a kind of quantile that divides the number of data points into four parts, or quarters.
- The first quartile (Q1) , is defined as the middle number between the smallest number and the median of the data set,
- The second quartile (Q2) is the median of the given data set.
- The third quartile (Q3) is the middle number between the median and the largest value of the data set.
Quartiles
Algorithm to find Quartiles
Here’s a step-by-step algorithm to find quartiles:
- Sort the dataset in ascending order.
- Calculate the total number of entries in the dataset.
- If the number of entries is even:
- Calculate the median (Q2) by taking the average of the two middle values.
- Divide the dataset into two halves: the first half containing the smallest n entries and the second half containing the largest n entries, where n = total number of entries / 2.
- Calculate Q1 as the median of the first half.
- Calculate Q3 as the median of the second half.
- If the number of entries is odd:
- Calculate the median (Q2) as the middle value.
- Divide the dataset into two halves: the first half containing the smallest n entries and the second half containing the largest n entries, where n = (total number of entries – 1) / 2.
- Calculate Q1 as the median of the first half.
- Calculate Q3 as the median of the second half.
- The calculated values of Q1, Q2, and Q3 represent the first quartile, median (second quartile), and third quartile respectively.
Range:
It is the difference between the largest value and the smallest value in the given data set.