Percentiles and quantiles in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of percentile calculation with scipy

What is the output of this code snippet that calculates the 75th percentile of the data array?

SciPy

import numpy as np
from scipy import stats

data = np.array([10, 20, 30, 40, 50])
result = stats.scoreatpercentile(data, 75)
print(result)

A 40.0

B 45.0

C 42.5

D 37.5

💡 Hint

Remember that the 75th percentile is the value below which 75% of the data fall. scipy's scoreatpercentile uses linear interpolation by default.

The 75th percentile lies between 30 and 40. Using linear interpolation, it is 30 + 0.75*(40-30) = 37.5.

❓ data_output

intermediate

Number of elements below the 60th percentile

Given this dataset, how many elements are below the 60th percentile calculated using scipy?

SciPy

import numpy as np
from scipy import stats

data = np.array([5, 15, 25, 35, 45, 55, 65])
percentile_60 = stats.scoreatpercentile(data, 60)
count_below = np.sum(data < percentile_60)
print(count_below)

A 3

B 4

C 5

D 6

💡 Hint

Calculate the 60th percentile value first, then count how many data points are strictly less than that value.

The 60th percentile is 41.0. Data points less than 41.0 are 5, 15, 25, 35 (4 elements).

❓ visualization

advanced

Visualizing quantiles with a boxplot

Which option produces a boxplot showing the quartiles of the data array using matplotlib and scipy?

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

data = np.array([12, 7, 3, 15, 8, 10, 6, 9, 11, 14])

q1 = stats.scoreatpercentile(data, 25)
q2 = stats.scoreatpercentile(data, 50)
q3 = stats.scoreatpercentile(data, 75)

plt.boxplot(data)
plt.title(f"Quartiles: Q1={q1}, Median={q2}, Q3={q3}")
plt.show()

A A boxplot with whiskers showing min and max, and a box from 7 to 12 with median at 9

B A boxplot with whiskers showing min and max, and a box from 6 to 15 with median at 10

C A boxplot with whiskers showing min and max, and a box from 7.25 to 11.75 with median at 9.5

D A boxplot with whiskers showing min and max, and a box from 3 to 15 with median at 9

💡 Hint

Check the quartile values calculated by scipy and compare with the boxplot box edges and median.

The 25th percentile (Q1) is 7.25, 50th percentile (median) is 9.5, and 75th percentile (Q3) is 11.75. The boxplot box edges correspond to Q1 and Q3, and the line inside is the median.

🧠 Conceptual

advanced

Understanding interpolation methods in percentile calculation

Which statement correctly describes the effect of changing the interpolation method in scipy's percentile calculation?

A Using 'nearest' interpolation always returns a data point from the dataset as the percentile value.

B Using 'higher' interpolation returns the smallest data point in the dataset.

C Using 'lower' interpolation averages the two closest data points around the percentile.

D Using 'linear' interpolation returns the closest data point without averaging.

💡 Hint

Think about how each interpolation method chooses the percentile value relative to the data points.

'Nearest' interpolation picks the closest actual data point to the percentile position. 'Linear' interpolates between points. 'Lower' picks the smaller data point at the percentile position. 'Higher' picks the larger data point.

🔧 Debug

expert

Identify the error in percentile calculation code

What error will this code raise when executed?

SciPy

import numpy as np
from scipy import stats

data = np.array([1, 2, 3, 4, 5])
result = stats.scoreatpercentile(data, 110)
print(result)

A ValueError: percentile must be in the range [0, 100]

B IndexError: index out of bounds

C TypeError: unsupported operand type(s)

D No error, outputs 5

💡 Hint

Percentiles must be between 0 and 100 inclusive.

Passing a percentile value greater than 100 causes a ValueError because percentiles are defined only between 0 and 100.