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.

Practice

1. What does the scipy.stats.describe function provide when applied to a dataset?

easy

A. Summary statistics like count, mean, variance, min, max, skewness, and kurtosis

B. Only the mean and median of the dataset

C. A plot showing data distribution

D. A list of unique values in the dataset

Solution

1. Step 1: Understand the purpose of scipy.stats.describe

   This function is designed to give a quick summary of key statistics about the data.

2. Step 2: Identify the statistics returned

   It returns count, mean, variance, minimum, maximum, skewness, and kurtosis, which describe data shape and spread.

3. Final Answer:

   Summary statistics like count, mean, variance, min, max, skewness, and kurtosis -> Option A

4. Quick Check:

   Descriptive stats = count, mean, variance, min, max, skewness, kurtosis [OK]

Hint: Remember: describe summarizes data with key stats [OK]

Common Mistakes:

• Thinking it returns only mean and median
• Confusing it with plotting functions
• Expecting a list of unique values

2. Which of the following is the correct way to import and use describe from scipy.stats?

easy

A. from scipy.stats import describe; result = describe(data)

B. import scipy.stats; result = describe(data)

C. from scipy import describe; result = describe(data)

D. import describe from scipy.stats; result = describe(data)

Solution

1. Step 1: Check correct import syntax for a function

   Functions are imported using from module import function syntax in Python.

2. Step 2: Verify usage of describe after import

   After importing, call describe(data) directly.

3. Final Answer:

   from scipy.stats import describe; result = describe(data) -> Option A

4. Quick Check:

   Correct import and call = from scipy.stats import describe; result = describe(data) [OK]

Hint: Use 'from scipy.stats import describe' to call directly [OK]

Common Mistakes:

• Using wrong import syntax like 'import describe from ...'
• Importing scipy.stats but not calling with module prefix
• Importing from wrong module

3. Given the code below, what will be the output for the mean and min values?

import numpy as np
from scipy.stats import describe

data = np.array([2, 4, 6, 8, 10])
result = describe(data)
print(result.mean, result.minmax[0])

medium

A. 6.0 0

B. 5.0 2

C. 6.0 2

D. 5.0 0

Solution

1. Step 1: Calculate the mean of the data array

   The data is [2, 4, 6, 8, 10]. Mean = (2+4+6+8+10)/5 = 30/5 = 6.0.

2. Step 2: Identify the minimum value from minmax

   minmax returns (min, max). The minimum is 2.

3. Final Answer:

   6.0 2 -> Option C

4. Quick Check:

   Mean = 6.0, Min = 2 [OK]

Hint: Mean is average; min is smallest value [OK]

Common Mistakes:

• Calculating mean incorrectly as 5.0
• Confusing minmax tuple order
• Assuming min is 0 without checking data

4. What is wrong with the following code snippet?

from scipy.stats import describe
data = [1, 2, 3, 4, 5]
result = describe(data, axis=1)
print(result)

medium

A. The print statement is missing parentheses

B. The data list should be converted to a numpy array first

C. The describe function requires a second argument for axis

D. Axis=1 is invalid for 1D data, causing an error

Solution

1. Step 1: Understand the data shape and axis parameter

   The data is a 1D list. Axis=1 means operate along columns of 2D or higher arrays.

2. Step 2: Identify the error caused by axis=1 on 1D data

   Using axis=1 on 1D data causes an AxisError because axis 1 does not exist.

3. Final Answer:

   Axis=1 is invalid for 1D data, causing an error -> Option D

4. Quick Check:

   Axis must exist in data shape [OK]

Hint: Check data dimensions before setting axis [OK]

Common Mistakes:

• Assuming axis=1 works for 1D data
• Thinking data must be numpy array for describe
• Ignoring Python 3 print syntax

5. You have a dataset with some zero and negative values: data = [0, -1, 2, 3, 4]. Using scipy.stats.describe, which statistic helps you understand if the data distribution is skewed?

hard

A. Variance

B. Skewness

C. Count

D. Minimum

Solution

1. Step 1: Recall what skewness measures

   Skewness shows if data is symmetric or leans left/right (skewed).

2. Step 2: Identify which statistic indicates skewness

   Among the options, only skewness directly measures data asymmetry.

3. Final Answer:

   Skewness -> Option B

4. Quick Check:

   Skewness = data asymmetry [OK]

Hint: Skewness shows data leaning direction [OK]

Common Mistakes:

• Confusing variance with skewness
• Thinking count or minimum show skewness
• Ignoring negative and zero values impact