Descriptive statistics (mean, median, std) in MATLAB - Mini Project: Build & Apply

Descriptive statistics (mean, median, std)

📖 Scenario: You are analyzing the daily sales numbers of a small store for one week. You want to understand the average sales, the middle value of sales, and how much the sales vary day to day.

🎯 Goal: Calculate the mean, median, and standard deviation of the daily sales data using MATLAB.

📋 What You'll Learn

Create a vector with the exact daily sales numbers

Create a variable to hold the number of days

Calculate mean, median, and standard deviation using MATLAB functions

Display the results clearly

💡 Why This Matters

🌍 Real World

Descriptive statistics help summarize and understand data quickly, such as daily sales, temperatures, or test scores.

💼 Career

Data analysts and scientists use these statistics to report insights and make decisions based on data patterns.

1

Create the daily sales data vector

Create a vector called sales with these exact daily sales numbers: [150, 200, 170, 220, 180, 210, 190]

MATLAB

% Create the sales vector with the exact values
% Your code here

Hint

Use square brackets [] to create a vector in MATLAB.

2

Create a variable for the number of days

Create a variable called num_days that stores the number of days by calculating the length of the sales vector using the length function.

MATLAB

sales = [150, 200, 170, 220, 180, 210, 190];
% Calculate the number of days in the sales vector
% Your code here

Hint

Use length(sales) to find how many elements are in the vector.

3

Calculate mean, median, and standard deviation

Calculate the mean of sales and store it in mean_sales. Calculate the median of sales and store it in median_sales. Calculate the standard deviation of sales and store it in std_sales. Use MATLAB functions mean, median, and std respectively.

MATLAB

sales = [150, 200, 170, 220, 180, 210, 190];
num_days = length(sales);
% Calculate mean, median, and standard deviation
% Your code here

Hint

Use mean(sales), median(sales), and std(sales) to calculate the statistics.

4

Display the results

Use fprintf to print the mean, median, and standard deviation values with descriptive text. Print each value on its own line with two decimal places.

MATLAB

sales = [150, 200, 170, 220, 180, 210, 190];
num_days = length(sales);
mean_sales = mean(sales);
median_sales = median(sales);
std_sales = std(sales);
% Display the results
% Your code here

Hint

Use fprintf with format '%.2f' to show two decimal places.

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