Percentiles and quantiles in SciPy - Step-by-Step Execution

Concept Flow - Percentiles and quantiles

Start with data array

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Sort data in ascending order

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Choose percentile or quantile value

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Calculate position in sorted data

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Interpolate if needed

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Return value at position

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End

We start with data, sort it, pick a percentile or quantile, find its position, interpolate if needed, and return the value.

Execution Sample

SciPy

import numpy as np
from scipy import stats

data = np.array([10, 20, 30, 40, 50])
percentile_40 = np.percentile(data, 40)
quantile_0_4 = np.quantile(data, 0.4)

Calculate the 40th percentile and 0.4 quantile of a small data array.

Execution Table

Step	Action	Data State	Calculation	Result
1	Start with data array	[10, 20, 30, 40, 50]	N/A	N/A
2	Sort data	[10, 20, 30, 40, 50]	Already sorted	[10, 20, 30, 40, 50]
3	Calculate 40th percentile position	N/A	pos = (40/100)*(5-1) = 1.6	Position 1.6
4	Interpolate between index 1 and 2	Values at 1=20, 2=30	20 + 0.6*(30-20)	26.0
5	Calculate 0.4 quantile position	N/A	pos = 0.4*(5-1) = 1.6	Position 1.6
6	Interpolate between index 1 and 2	Values at 1=20, 2=30	20 + 0.6*(30-20)	26.0
7	Return results	N/A	N/A	percentile_40 = 26.0, quantile_0_4 = 26.0
8	End	N/A	N/A	Calculation complete

💡 Finished calculating requested percentile and quantile values.

Variable Tracker

Variable	Start	After Step 3	After Step 4	After Step 5	After Step 6	Final
data	[10,20,30,40,50]	[10,20,30,40,50]	[10,20,30,40,50]	[10,20,30,40,50]	[10,20,30,40,50]	[10,20,30,40,50]
percentile_40	N/A	N/A	26.0	26.0	26.0	26.0
quantile_0_4	N/A	N/A	N/A	N/A	26.0	26.0

Key Moments - 2 Insights

Why do we interpolate between two data points for the percentile?

Because the calculated position is not an integer index, we find the value between two points to get a precise percentile value, as shown in steps 3 and 4.

Are percentile and quantile calculations different here?

No, both use the same position calculation and interpolation method, so the 40th percentile and 0.4 quantile give the same result, as seen in steps 3-6.

Visual Quiz - 3 Questions

Look at the execution table, what is the calculated position for the 40th percentile?

A 2.0

B 1.6

C 0.4

D 4.0

💡 Hint

Check Step 3 in the execution table where position is calculated.

At which step do we interpolate between data points?

A Step 2

B Step 6

C Step 4

D Step 7

💡 Hint

Look for where values at indices 1 and 2 are used for interpolation.

If the data array had 10 elements instead of 5, how would the position for the 40th percentile change?

A It would be 3.6

B It would be 4.0

C It would be 1.6

D It would be 0.4

💡 Hint

Position = (percentile/100)*(n-1), so with n=10, calculate accordingly.

Concept Snapshot

Percentiles and quantiles find data values below a given percentage.
Sort data first.
Position = percentile/quantile * (n-1).
Interpolate if position is not whole.
Use numpy.percentile or numpy.quantile for easy calculation.

Full Transcript

We start with a data array and sort it. To find a percentile or quantile, we calculate its position in the sorted data using the formula position = (percentile/100) * (n-1) or position = quantile * (n-1). If the position is not an integer, we interpolate between the two closest data points. For example, the 40th percentile of [10,20,30,40,50] is at position 1.6, so we interpolate between the values at index 1 (20) and index 2 (30), resulting in 26.0. The same applies for the 0.4 quantile. This method gives a precise value representing the percentile or quantile in the data.