Descriptive statistics (mean, median, std) in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Calculate mean, median, and standard deviation

What is the output of the following MATLAB code calculating mean, median, and standard deviation of the vector A?

MATLAB

A = [2, 4, 6, 8, 10];
mean_val = mean(A);
median_val = median(A);
std_val = std(A);
result = [mean_val, median_val, std_val];

A [5 6 3.1623]

B [6 5 3.1623]

C [6 6 2.8284]

D [6 6 3.1623]

💡 Hint

Recall that mean and median are measures of central tendency, and std is the spread.

The mean and median of the vector [2,4,6,8,10] are both 6 because the data is symmetric. The standard deviation is approximately 3.1623.

❓ data_output

intermediate

Number of elements above mean

Given the vector B = [1, 3, 5, 7, 9, 11], how many elements are strictly greater than the mean of B?

MATLAB

B = [1, 3, 5, 7, 9, 11];
mean_B = mean(B);
count_above_mean = sum(B > mean_B);

A 4

B 2

C 3

D 1

💡 Hint

Calculate the mean first, then count elements greater than it.

The mean of B is 6. Elements greater than 6 are 7, 9, and 11, so count is 3.

🔧 Debug

advanced

Identify the error in standard deviation calculation

What error will the following MATLAB code produce?

MATLAB

C = [4, 8, 12, 16];
std_val = std(C, 1);

A No error, std_val is calculated using population std

B Error: std function requires two output arguments

C Error: std function does not accept second argument

D Error: Variable C is undefined

💡 Hint

Check MATLAB documentation for std function syntax.

The second argument '1' tells MATLAB to compute the population standard deviation. This is valid syntax and produces no error.

🧠 Conceptual

advanced

Effect of outliers on mean and median

Which statement correctly describes the effect of an extreme outlier on the mean and median of a dataset?

A Both mean and median are equally affected by outliers

B Mean is more affected by outliers than median

C Median is more affected by outliers than mean

D Neither mean nor median is affected by outliers

💡 Hint

Think about which measure is sensitive to extreme values.

Mean is sensitive to extreme values because it averages all data points, while median depends on the middle value and is more robust.

🚀 Application

expert

Calculate mean and std ignoring NaN values

Given the vector D = [3, NaN, 7, 9, NaN, 5], which MATLAB code correctly calculates the mean and standard deviation ignoring NaN values?

A mean_D = mean(D(~isnan(D))); std_D = std(D(~isnan(D)));

B mean_D = mean(D); std_D = std(D);

C mean_D = mean(D, 'includenan'); std_D = std(D, 'includenan');

D mean_D = mean(D, 'omitnan'); std_D = std(D, 'omitnan');

💡 Hint

Check how to exclude NaN values in MATLAB calculations.

Option A manually filters out NaN values before calculating mean and std, which works in all MATLAB versions. Option A uses 'omitnan' flag, a feature introduced in later MATLAB releases.

Practice

1. What does the mean function calculate in MATLAB when applied to a numeric array?

easy

A. The difference between the largest and smallest values

B. The middle value after sorting the array

C. The total sum of all elements in the array

D. The average value of all elements in the array

Solution

1. Step 1: Understand the mean function

   The mean function calculates the average by adding all elements and dividing by the number of elements.

2. Step 2: Compare with other statistics

   Median is the middle value, not the average. Sum is total, not average. Range is difference, not average.

3. Final Answer:

   The average value of all elements in the array -> Option D

4. Quick Check:

   Mean = Average [OK]

Hint: Mean is the sum divided by count [OK]

Common Mistakes:

• Confusing mean with median
• Thinking mean is the sum only
• Mixing mean with range

2. Which of the following is the correct MATLAB syntax to calculate the standard deviation of a vector data?

easy

A. median(data)

B. standard_deviation(data)

C. std(data)

D. mean(data)

Solution

1. Step 1: Recall MATLAB function names

   MATLAB uses std() to calculate standard deviation, not standard_deviation().

2. Step 2: Eliminate incorrect options

   mean() calculates average, median() calculates middle value, so both are incorrect for standard deviation.

3. Final Answer:

   std(data) -> Option C

4. Quick Check:

   Standard deviation function is std() [OK]

Hint: Use std() for standard deviation in MATLAB [OK]

Common Mistakes:

• Using mean() instead of std()
• Typing non-existent function standard_deviation()
• Confusing median() with std()

3. What is the output of the following MATLAB code?

data = [3, 7, 5, 9, 1];
m = median(data);
s = std(data);
[m, s]

medium

A. [5, 2.8284]

B. [5, 3.1623]

C. [7, 3.1623]

D. [3, 2.8284]

Solution

1. Step 1: Calculate the median of data

   Sorted data is [1, 3, 5, 7, 9]. The middle value is 5, so median = 5.

2. Step 2: Calculate the standard deviation

   Mean = (3+7+5+9+1)/5 = 5. Differences squared: (3-5)^2=4, (7-5)^2=4, (5-5)^2=0, (9-5)^2=16, (1-5)^2=16. Sum = 40, variance = 40/4 = 10 (using n-1 for std), std = sqrt(10) ≈ 3.1623.

3. Final Answer:

   [5, 3.1623] -> Option B

4. Quick Check:

   Median = 5, Std ≈ 3.16 [OK]

Hint: Median is middle; std uses n-1 in denominator [OK]

Common Mistakes:

• Using n instead of n-1 for std denominator
• Mixing mean and median values
• Incorrectly sorting data for median

4. Identify the error in this MATLAB code snippet that calculates the mean and median of values:

values = [10, 20, 30, 40];
mean_val = mean(values)
median_val = median(values

medium

A. Missing closing parenthesis in median function call

B. Using mean instead of median for median_val

C. Incorrect variable name 'values'

D. No error, code runs fine

Solution

1. Step 1: Check syntax of median function call

   The line median_val = median(values is missing a closing parenthesis.

2. Step 2: Confirm other parts are correct

   mean(values) is correct, variable name is consistent, so no other errors.

3. Final Answer:

   Missing closing parenthesis in median function call -> Option A

4. Quick Check:

   Syntax error due to missing ')' [OK]

Hint: Check all parentheses in function calls [OK]

Common Mistakes:

• Ignoring missing parenthesis errors
• Confusing mean and median functions
• Assuming variable name errors without checking

5. Given a dataset data = [2, 4, 4, 4, 5, 5, 7, 9], which MATLAB code correctly calculates the mean, median, and standard deviation and stores them in variables m, med, s respectively?

hard

A. m = mean(data); med = median(data); s = std(data);

B. m = median(data); med = mean(data); s = std(data);

C. m = std(data); med = mean(data); s = median(data);

D. m = mean(data); med = std(data); s = median(data);

Solution

1. Step 1: Match variables to correct functions

   Variable m should hold mean, med median, s standard deviation.

2. Step 2: Verify correct function usage

   m = mean(data); med = median(data); s = std(data); assigns mean to m, median to med, std to s, which is correct.

3. Final Answer:

   m = mean(data); med = median(data); s = std(data); -> Option A

4. Quick Check:

   Correct variable-function mapping [OK]

Hint: Assign mean, median, std to matching variable names [OK]

Common Mistakes:

• Swapping mean and median assignments
• Assigning std to median variable
• Mixing variable names and functions