Descriptive statistics (mean, median, std) in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the mean of the data vector.

MATLAB

data = [5, 10, 15, 20, 25];
mean_value = [1](data);

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

Astd

Bmean

Cmedian

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'median' instead of 'mean' will give the middle value, not the average.

Using 'std' will calculate the spread, not the average.

The mean function calculates the average value of the data vector.

2fill in blank

medium

Complete the code to calculate the median of the data vector.

MATLAB

data = [3, 7, 9, 2, 5];
median_value = [1](data);

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

Amedian

Bmean

Cstd

Dmax

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'mean' will calculate the average, not the middle value.

Using 'std' calculates spread, not the middle value.

The median function finds the middle value when data is sorted.

3fill in blank

hard

Fix the error in the code to calculate the standard deviation of the data vector.

MATLAB

data = [4, 8, 12, 16, 20];
std_dev = [1](data);

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

Amean

Bmedian

Cvar

Dstd

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'var' returns variance, not standard deviation.

Using 'mean' or 'median' does not measure spread.

The std function calculates the standard deviation, which measures spread.

4fill in blank

hard

Fill both blanks to create a structure with mean and median of the data vector.

MATLAB

data = [2, 4, 6, 8, 10];
stats = struct('mean', [1](data), 'median', [2](data));

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

Amean

Bmedian

Cstd

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping mean and median functions.

Using 'std' or 'sum' instead of mean or median.

The struct function creates a structure with fields. Use mean and median to fill the fields.

5fill in blank

hard

Fill all three blanks to create a structure with mean, median, and standard deviation of the data vector.

MATLAB

data = [1, 3, 5, 7, 9];
stats = struct('mean', [1](data), 'median', [2](data), 'std_dev', [3](data));

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

Amedian

Bmean

Cstd

Dsum

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up mean and median.

Using 'sum' instead of 'std' for spread.

Use mean for average, median for middle value, and std for standard deviation.

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