Percentiles and quantiles in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the 50th percentile of the data array using scipy.

SciPy

from scipy import stats
import numpy as np
data = np.array([10, 20, 30, 40, 50])
percentile_50 = stats.scoreatpercentile(data, [1])
print(percentile_50)

Drag options to blanks, or click blank then click option'

A25

B50

C75

D100

Attempts:

3 left

💡 Hint

Common Mistakes

Using 25 or 75 instead of 50 for the median percentile.

Confusing percentile value with data values.

The 50th percentile corresponds to the median value, so we use 50 as the percentile value.

2fill in blank

medium

Complete the code to calculate the 0.25 quantile (25th percentile) of the data using scipy's percentile function.

SciPy

from scipy import stats
import numpy as np
data = np.array([5, 15, 25, 35, 45])
quantile_25 = stats.scoreatpercentile(data, [1])
print(quantile_25)

Drag options to blanks, or click blank then click option'

A0.25

B0.75

C25

D75

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0.25 instead of 25 for the percentile argument.

Mixing up 25th and 75th percentiles.

The 25th percentile corresponds to the 0.25 quantile, but scipy expects percentile values between 0 and 100, so use 25.

3fill in blank

hard

Fix the error in the code to correctly calculate the 75th percentile using scipy.

SciPy

from scipy import stats
import numpy as np
data = np.array([2, 4, 6, 8, 10])
percentile_75 = stats.scoreatpercentile(data, [1])
print(percentile_75)

Drag options to blanks, or click blank then click option'

A75

B0.75

C7.5

D0.25

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0.75 instead of 75.

Using a data value instead of percentile value.

Percentiles in scipy are given as values between 0 and 100, so 75 is correct for the 75th percentile.

4fill in blank

hard

Fill both blanks to create a dictionary of word lengths for words longer than 3 characters.

SciPy

words = ['apple', 'bat', 'carrot', 'dog', 'elephant']
lengths = {word: [1] for word in words if len(word) [2] 3}
print(lengths)

Drag options to blanks, or click blank then click option'

Alen(word)

B>

C<

Dword

Attempts:

3 left

💡 Hint

Common Mistakes

Using word instead of len(word) for the value.

Using < instead of > in the condition.

We want the length of each word (len(word)) and only include words longer than 3 characters (len(word) > 3).

5fill in blank

hard

Fill all three blanks to create a dictionary of uppercase words and their lengths for words longer than 4 characters.

SciPy

words = ['apple', 'bat', 'carrot', 'dog', 'elephant']
result = { [1]: [2] for word in words if len(word) [3] 4 }
print(result)

Drag options to blanks, or click blank then click option'

Aword.upper()

Blen(word)

C>

Dword

Attempts:

3 left

💡 Hint

Common Mistakes

Using word instead of word.upper() for keys.

Using < instead of > in the condition.

The dictionary keys are uppercase words (word.upper()), values are lengths (len(word)), and we filter words longer than 4 characters (len(word) > 4).

Practice

1. What does the 90th percentile represent in a dataset?

easy

A. The average of the top 90% of data

B. The value below which 90% of the data falls

C. The value above which 90% of the data falls

D. The middle value of the dataset

Solution

1. Step 1: Understand percentile definition

   A percentile indicates the value below which a given percentage of observations fall.

2. Step 2: Apply to 90th percentile

   The 90th percentile means 90% of data points are below this value.

3. Final Answer:

   The value below which 90% of the data falls -> Option B

4. Quick Check:

   Percentile = value below % data [OK]

Hint: Percentile = value below that percent of data [OK]

Common Mistakes:

• Confusing percentile with average
• Thinking percentile is value above percentage
• Mixing percentile with median

2. Which of the following is the correct way to find the 25th percentile using scipy.stats?

easy

A. stats.quantile(data, 25)

B. stats.percentile(data, 0.25)

C. stats.mquantiles(data, prob=0.25)

D. stats.scoreatpercentile(data, 25)

Solution

1. Step 1: Recall scipy function for percentile

   The function to find percentile is stats.scoreatpercentile with arguments (data, percentile).

2. Step 2: Check options

   stats.scoreatpercentile(data, 25) uses stats.scoreatpercentile(data, 25), which is correct for 25th percentile.

3. Final Answer:

   stats.scoreatpercentile(data, 25) -> Option D

4. Quick Check:

   Use scoreatpercentile for percentiles [OK]

Hint: Use stats.scoreatpercentile(data, percentile) [OK]

Common Mistakes:

• Using wrong function names like percentile or quantile
• Passing 0.25 instead of 25 for percentile
• Confusing quantiles with percentiles

3. Given the data array [10, 20, 30, 40, 50], what is the output of stats.scoreatpercentile(data, 40)?

medium

A. 26.0

B. 22.0

C. 30.0

D. 20.0

Solution

1. Step 1: Understand percentile calculation

   40th percentile means the value below which 40% of data lies. Data sorted: [10, 20, 30, 40, 50].

2. Step 2: Calculate 40th percentile using interpolation

   Position = (40/100)*(n-1) = 0.4*4 = 1.6. Interpolate between data[1]=20 and data[2]=30: 20 + 0.6*(30-20) = 20 + 6 = 26.0.

3. Final Answer:

   26.0 -> Option A

4. Quick Check:

   Interpolation gives 26.0 [OK]

Hint: Percentile position = p/100*(n-1), interpolate values [OK]

Common Mistakes:

• Choosing nearest data point without interpolation
• Using index p instead of p/100*(n-1)
• Confusing percentile with median

4. The code below is intended to find the quartiles of data using scipy but raises an error. What is the error?

import scipy.stats as stats
data = [5, 10, 15, 20, 25]
quartiles = stats.mstats.mquantiles(data, prob=[0.25, 0.5, 0.75])
print(quartiles)

medium

A. mquantiles requires numpy array, not list

B. prob argument should be a single float, not a list

C. No error, code runs correctly

D. mquantiles is not in scipy.stats.mstats

Solution

1. Step 1: Check function location and usage

   stats.mstats.mquantiles is a valid function and accepts prob as a list for multiple quantiles.

2. Step 2: Check input data type

   mquantiles accepts list or array-like data, so list input is valid.

3. Final Answer:

   No error, code runs correctly -> Option C

4. Quick Check:

   mquantiles accepts list and prob list [OK]

Hint: mquantiles accepts list and prob list [OK]

Common Mistakes:

• Assuming mquantiles only accepts numpy arrays
• Thinking prob must be a single float
• Confusing function location in scipy

5. You have a dataset of exam scores: [55, 70, 65, 80, 90, 85, 75]. You want to divide the scores into four equal groups (quartiles) using scipy. Which code snippet correctly computes the quartiles?

hard

A. stats.mstats.mquantiles(scores, prob=[0.25, 0.5, 0.75])

B. stats.scoreatpercentile(scores, [25, 50, 75])

C. np.percentile(scores, [0.25, 0.5, 0.75])

D. stats.mstats.mquantiles(scores, prob=[25, 50, 75])

Solution

1. Step 1: Identify correct function for quartiles

   Quartiles are quantiles at 25%, 50%, and 75%. stats.mstats.mquantiles accepts prob as fractions between 0 and 1.

2. Step 2: Check options for correct prob format

   stats.mstats.mquantiles(scores, prob=[0.25, 0.5, 0.75]) uses prob=[0.25, 0.5, 0.75], which is correct. stats.scoreatpercentile(scores, [25, 50, 75]) uses scoreatpercentile but with a list, which is invalid. np.percentile(scores, [0.25, 0.5, 0.75]) uses numpy but with fractions instead of percentages. stats.mstats.mquantiles(scores, prob=[25, 50, 75]) uses prob with values >1, which is invalid.

3. Final Answer:

   stats.mstats.mquantiles(scores, prob=[0.25, 0.5, 0.75]) -> Option A

4. Quick Check:

   mquantiles prob values are fractions [OK]

Hint: Use mquantiles with prob as fractions (0.25, 0.5, 0.75) [OK]

Common Mistakes:

• Passing percent values instead of fractions to prob
• Using scoreatpercentile with list of percentiles
• Confusing numpy percentile input format