Descriptive statistics (describe) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of scipy.stats.describe on a simple array

What is the output of the following code snippet using scipy.stats.describe on a simple numeric array?

SciPy

from scipy.stats import describe
import numpy as np

arr = np.array([1, 2, 3, 4, 5])
result = describe(arr)
print(result)

A DescribeResult(nobs=5, minmax=(1, 5), mean=3.0, variance=2.5, skewness=0.0, kurtosis=-1.3)

B DescribeResult(nobs=5, minmax=(1, 5), mean=3.0, variance=2.0, skewness=0.0, kurtosis=-1.3)

C )3.1-=sisotruk ,0.0=ssenweks ,5.2=ecnairav ,0.3=naem ,)5 ,1(=xamnim ,5=sbon(tluseRebircseD

D DescribeResult(nobs=5, minmax=(1, 5), mean=3.0, variance=2.5, skewness=0.0, kurtosis=0.0)

💡 Hint

Recall that variance is calculated with denominator n-1 by default in scipy.stats.describe.

The describe function returns a named tuple with statistics. For the array [1,2,3,4,5], the variance is 2.5 (sample variance), skewness is 0 (symmetrical data), and kurtosis is -1.3 (platykurtic).

❓ data_output

intermediate

Number of observations from describe on 2D array

Given the following 2D array, what is the number of observations (nobs) reported by scipy.stats.describe when applied along axis=1?

SciPy

from scipy.stats import describe
import numpy as np

arr = np.array([[1, 2, 3], [4, 5, 6]])
result = [describe(row).nobs for row in arr]
print(result)

A [6, 6]

B [1, 1]

C [3, 3]

D [2, 2]

💡 Hint

Each row has 3 elements, so nobs per row is 3.

When applying describe to each row, the number of observations is the length of that row, which is 3 for both rows.

🔧 Debug

advanced

Identify the error in using describe on a list with mixed types

What error will the following code raise when using scipy.stats.describe on a list with mixed types?

SciPy

from scipy.stats import describe
mixed_list = [1, 'two', 3]
describe(mixed_list)

A TypeError: unsupported operand type(s) for -: 'str' and 'int'

B ValueError: could not convert string to float: 'two'

C TypeError: object of type 'str' has no len()

D No error, returns descriptive statistics ignoring strings

💡 Hint

The function tries to perform numeric operations on all elements.

The describe function attempts to compute variance and mean, which involves subtraction. Since 'two' is a string, subtracting it from an int causes a TypeError.

🧠 Conceptual

advanced

Understanding kurtosis output from describe

Which statement correctly describes the kurtosis value returned by scipy.stats.describe?

A Kurtosis is the same as variance but scaled differently

B Kurtosis is the excess kurtosis, where 0 means normal distribution kurtosis

C Kurtosis is the raw fourth moment without adjustment

D Kurtosis is always positive and measures skewness

💡 Hint

Think about what excess kurtosis means in statistics.

The describe function returns excess kurtosis, which is kurtosis minus 3. A value of 0 means the distribution has the same kurtosis as a normal distribution.

🚀 Application

expert

Calculate skewness from describe output

You have the following output from scipy.stats.describe on a dataset: DescribeResult(nobs=4, minmax=(2, 10), mean=6.5, variance=12.33, skewness=1.2, kurtosis=0.5). What does the skewness value tell you about the data distribution?

A Skewness value indicates the data has no outliers

B The data is perfectly symmetrical with no skew

C The data is skewed to the left, meaning a longer tail on the lower values

D The data is skewed to the right, meaning a longer tail on the higher values

💡 Hint

Positive skewness means the tail is on the right side.

A skewness value greater than 0 means the distribution has a longer or fatter tail on the right side (higher values). This indicates right skewness.