Descriptive statistics (mean, median, std) in MATLAB - Step-by-Step Execution

Concept Flow - Descriptive statistics (mean, median, std)

Start with data array

↓

Calculate Mean

↓

Calculate Median

↓

Calculate Standard Deviation

↓

Output all three statistics

The flow starts with a data set, then calculates mean, median, and standard deviation step-by-step, and finally outputs these values.

Execution Sample

MATLAB

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

This code calculates the mean, median, and standard deviation of a simple data array.

Execution Table

Step	Variable	Operation	Value
1	data	Initialize data array	[2 4 6 8 10]
2	mean_val	Calculate mean(data)	6
3	median_val	Calculate median(data)	6
4	std_val	Calculate std(data)	3.1623
5	result	Combine mean, median, std	[6 6 3.1623]

💡 All descriptive statistics calculated and combined into result array.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	Final
data	[2 4 6 8 10]	[2 4 6 8 10]	[2 4 6 8 10]	[2 4 6 8 10]	[2 4 6 8 10]
mean_val	undefined	6	6	6	6
median_val	undefined	undefined	6	6	6
std_val	undefined	undefined	undefined	3.1623	3.1623
result	undefined	undefined	undefined	undefined	[6 6 3.1623]

Key Moments - 3 Insights

Why is the mean and median the same in this example?

Because the data is symmetric and evenly spaced, both mean and median equal 6 as shown in steps 2 and 3 of the execution table.

What does the standard deviation value represent here?

It shows how spread out the data is from the mean. Step 4 calculates std as about 3.1623, meaning data points vary on average by this amount from the mean.

Why do we combine mean, median, and std into one result array?

To easily output and use all three statistics together, as shown in step 5 of the execution table.

Visual Quiz - 3 Questions

Look at the execution table, what is the value of mean_val after step 2?

A 3.1623

B 4

C 6

D undefined

💡 Hint

Check the 'mean_val' value in row with Step 2 in the execution_table.

At which step is the standard deviation calculated?

A Step 2

B Step 4

C Step 3

D Step 5

💡 Hint

Look for the row where 'std_val' is assigned a value in the execution_table.

If the data array changed to [1, 1, 1, 1, 1], what would the standard deviation be?

A 0

B 1

C 5

D Undefined

💡 Hint

Standard deviation measures spread; identical values mean zero spread.

Concept Snapshot

Descriptive statistics summarize data:
- mean(data): average value
- median(data): middle value
- std(data): spread from mean
Use MATLAB functions mean(), median(), std()
Combine results for easy use.

Full Transcript

We start with a data array. Then we calculate the mean, which is the average of all numbers. Next, we find the median, the middle number when data is sorted. After that, we calculate the standard deviation, which tells us how spread out the numbers are from the mean. Finally, we put all three results together to see them at once. This process helps us understand the main features of the data quickly.

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