Descriptive statistics review in Data Analysis Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the mean in descriptive statistics?

The mean is the average value of a dataset. You add all numbers together and divide by how many numbers there are.

beginner

What does the median represent in a dataset?

The median is the middle value when the data is sorted from smallest to largest. It splits the data into two equal halves.

intermediate

Explain the difference between variance and standard deviation.

Variance measures how spread out the data is by averaging the squared differences from the mean. Standard deviation is the square root of variance and shows spread in the original units.

intermediate

What is the purpose of the interquartile range (IQR)?

IQR measures the middle 50% spread of the data. It is the difference between the 75th percentile (Q3) and the 25th percentile (Q1). It helps identify outliers.

intermediate

How does skewness describe a dataset?

Skewness shows if the data leans more to one side. Positive skew means a longer tail on the right, negative skew means a longer tail on the left.

Which measure of central tendency is least affected by extreme values?

A Mean

B Median

C Mode

D Range

The median is the middle value and is not affected by very high or low values, unlike the mean.

What does a high standard deviation indicate about a dataset?

A Data points are spread out from the mean

B Data points are close to the mean

C Data has no variation

D Data is skewed

A high standard deviation means data points are more spread out from the average.

The interquartile range (IQR) is calculated as:

A Q1 - Q3

B Mean - Median

C Q3 - Q1

D Max - Min

IQR is the difference between the 75th percentile (Q3) and the 25th percentile (Q1).

If a dataset has a skewness close to zero, it means:

A Data is perfectly symmetrical

B Data is heavily skewed right

C Data is heavily skewed left

D Data has many outliers

Skewness near zero means the data distribution is roughly symmetrical.

Which descriptive statistic tells you the most frequent value in a dataset?

A Mean

B Median

C Variance

D Mode

Mode is the value that appears most often in the data.

Describe the main measures of central tendency and when to use each.

Think about average, middle value, and most common value.

Explain how spread or variability in data is measured and why it matters.

Consider how data points differ from the average.

Practice

1. Which of the following best describes the median in a dataset?

easy

A. The middle value when data is sorted from smallest to largest

B. The most frequently occurring value in the data

C. The average of all values in the data

D. The difference between the largest and smallest values

Solution

1. Step 1: Understand what median means

   The median is the value that lies in the middle of a sorted list of numbers.

2. Step 2: Compare with other options

   Mode is the most frequent value, mean is the average, and range is max-min.

3. Final Answer:

   The middle value when data is sorted from smallest to largest -> Option A

4. Quick Check:

   Median = middle value [OK]

Hint: Median splits sorted data in half [OK]

Common Mistakes:

• Confusing median with mean
• Thinking median is the most frequent value
• Mixing median with range

2. Which of the following is the correct way to get descriptive statistics of a pandas DataFrame df?

easy

A. describe(df)

B. df.summary()

C. df.describe()

D. df.stats()

Solution

1. Step 1: Recall pandas method for summary

   In pandas, describe() is the method to get descriptive stats.

2. Step 2: Check other options

   Methods like summary(), stats() do not exist in pandas, and describe(df) is not valid syntax.

3. Final Answer:

   df.describe() -> Option C

4. Quick Check:

   Use df.describe() for stats [OK]

Hint: Use df.describe() for quick stats [OK]

Common Mistakes:

• Using non-existent methods like summary()
• Calling describe as a function with df argument
• Confusing with other libraries

3. Given the following code, what will be the output of print(df.mean())?

import pandas as pd
data = {'A': [1, 2, 3], 'B': [4, 5, 6]}
df = pd.DataFrame(data)

medium

A. A 2.0
B 5.0
dtype: float64

B. A 3.0
B 6.0
dtype: int64

C. A 1.5
B 4.5
dtype: float64

D. Error: mean() not defined

Solution

1. Step 1: Calculate mean for each column

   Column A values: 1, 2, 3; mean = (1+2+3)/3 = 2.0. Column B values: 4, 5, 6; mean = (4+5+6)/3 = 5.0.

2. Step 2: Understand pandas output format

   Printing df.mean() shows means per column with dtype float64.

3. Final Answer:

   A 2.0 B 5.0 dtype: float64 -> Option A

4. Quick Check:

   Mean = sum/number of values [OK]

Hint: Mean = sum of values divided by count [OK]

Common Mistakes:

• Calculating median instead of mean
• Mixing up column values
• Expecting integer dtype instead of float

4. The following code is intended to calculate the standard deviation of column 'X' in DataFrame df. What is the error?

import pandas as pd
data = {'X': [10, 20, 30, 40]}
df = pd.DataFrame(data)
std_dev = df.std('X')
print(std_dev)

medium

A. DataFrame std() method requires axis=1 argument

B. The std() method does not take any arguments; column must be selected first

C. The code should use df['X'].variance() instead

D. No error; code runs correctly

Solution

1. Step 1: Check std() method usage

   In pandas, std() calculates standard deviation for all numeric columns or Series. It does not accept a column name as argument.

2. Step 2: Correct way to get std of column 'X'

   We must select the column first: df['X'].std().

3. Final Answer:

   The std() method does not take any arguments; column must be selected first -> Option B

4. Quick Check:

   Use df['X'].std() to get column std [OK]

Hint: Select column before std() call [OK]

Common Mistakes:

• Passing column name as argument to std()
• Using variance() instead of std()
• Assuming std() needs axis=1

5. You have a DataFrame df with columns 'Age' and 'Salary'. You want to find the average salary for people older than 30. Which code correctly does this?

hard

A. df['Salary'].mean(df['Age'] > 30)

B. df['Salary'].mean().filter(df['Age'] > 30)

C. df.mean()['Salary'][df['Age'] > 30]

D. df[df['Age'] > 30]['Salary'].mean()

Solution

1. Step 1: Filter rows where Age > 30

   Use boolean indexing: df[df['Age'] > 30] selects rows with Age greater than 30.

2. Step 2: Select 'Salary' column and calculate mean

   From filtered rows, select 'Salary' column and call mean() to get average salary.

3. Final Answer:

   df[df['Age'] > 30]['Salary'].mean() -> Option D

4. Quick Check:

   Filter then mean for conditional average [OK]

Hint: Filter rows first, then calculate mean [OK]

Common Mistakes:

• Passing condition inside mean()
• Trying to filter after mean()
• Using mean() on entire DataFrame