Why statistical tools drive decisions in MATLAB - Challenge Your Understanding

Challenge - 5 Problems

❓ Predict Output

intermediate

Understanding mean and median impact

What is the output of this MATLAB code that calculates mean and median of a dataset?

MATLAB

data = [1 2 2 3 100];
mean_val = mean(data);
median_val = median(data);
fprintf('Mean: %.2f, Median: %.2f\n', mean_val, median_val);

A Mean: 21.60, Median: 2.00

B Mean: 21.60, Median: 3.00

C Mean: 21.60, Median: 100.00

D Mean: 2.00, Median: 2.00

💡 Hint

Recall how mean sums all values and divides by count, median is the middle value after sorting.

The mean sums all numbers (1+2+2+3+100=108) and divides by 5, giving 21.6. The median is the middle value in sorted order [1 2 2 3 100], which is 2.

❓ Predict Output

intermediate

Effect of outliers on variance

What is the output of this MATLAB code that calculates variance of two datasets?

MATLAB

data1 = [10 12 11 13 12];
data2 = [10 12 11 13 120];
var1 = var(data1);
var2 = var(data2);
fprintf('Variance1: %.2f, Variance2: %.2f\n', var1, var2);

A Variance1: 0.00, Variance2: 2355.70

B Variance1: 1.30, Variance2: 1.30

C Variance1: 2355.70, Variance2: 1.30

D Variance1: 1.30, Variance2: 2355.70

💡 Hint

Variance measures spread; a large outlier increases variance significantly.

The first dataset has small spread, variance about 1.3. The second dataset has a large outlier (120), increasing variance drastically to about 2355.7.

🔧 Debug

advanced

Identify the error in hypothesis testing code

What error does this MATLAB code produce when running a t-test?

MATLAB

sample1 = [5.1 5.5 5.3 5.7];
sample2 = [5.0 5.2 5.4];
[h,p] = ttest2(sample1, sample2, 'Alpha', 0.05, 'Tail', 'right');
disp(['p-value: ' num2str(p)]);

A No error, outputs p-value correctly

B Error: Inputs must be vectors of equal length

C Error: Invalid alpha value

D Error: Unrecognized parameter name 'Tail'

💡 Hint

Check MATLAB documentation for correct parameter names in ttest2.

There is no error in the code. ttest2 supports unequal sample sizes and the parameters 'Alpha' and 'Tail' are used correctly. It performs a right-tailed t-test and displays the p-value.

❓ Predict Output

advanced

Interpreting correlation coefficient output

What is the output of this MATLAB code that calculates correlation coefficient?

MATLAB

x = [1 2 3 4 5];
y = [2 4 6 8 10];
r = corrcoef(x,y);
fprintf('Correlation coefficient: %.2f\n', r(1,2));

A Correlation coefficient: -1.00

B Correlation coefficient: 1.00

C Correlation coefficient: 0.00

D Correlation coefficient: 0.50

💡 Hint

Correlation measures linear relationship; y is exactly twice x.

Since y is exactly 2 times x, the correlation coefficient is 1, indicating perfect positive linear correlation.

🧠 Conceptual

expert

Why do statistical tools drive better decisions?

Which option best explains why statistical tools improve decision-making in data analysis?

A They eliminate the need for human judgment in all decisions.

B They guarantee 100% accurate predictions about future events.

C They provide objective measures to understand data patterns and variability, reducing guesswork.

D They always simplify data by removing all outliers and anomalies.

💡 Hint

Think about how statistics help interpret data rather than replace judgment.

Statistical tools help quantify data characteristics and variability, giving objective insights that reduce guesswork. They do not guarantee perfect predictions or remove the need for human judgment.

Practice

1. Why do we use statistical tools like mean and std in MATLAB when making decisions?

easy

A. To make the code run faster

B. To change the data values randomly

C. To understand data patterns and make informed decisions

D. To create graphics only

Solution

1. Step 1: Understand the purpose of statistical tools

   Statistical tools like mean and standard deviation help summarize data and show patterns.

2. Step 2: Connect tools to decision making

   By understanding data patterns, we can make better, informed decisions rather than guessing.

3. Final Answer:

   To understand data patterns and make informed decisions -> Option C

4. Quick Check:

   Statistical tools guide decisions = B [OK]

Hint: Statistical tools summarize data to guide decisions [OK]

Common Mistakes:

• Thinking statistical tools speed up code
• Believing they randomly change data
• Assuming they only create graphics

2. Which MATLAB command correctly calculates the average of the vector A = [4, 8, 12]?

easy

A. average(A)

B. mean(A)

C. sum(A)

D. std(A)

Solution

1. Step 1: Identify the function for average in MATLAB

   The function mean() calculates the average of numbers in a vector.

2. Step 2: Check other options

   average() is not a MATLAB function, sum() adds values, and std() calculates standard deviation.

3. Final Answer:

   mean(A) -> Option B

4. Quick Check:

   Average = mean() [OK]

Hint: Use mean() to find average in MATLAB [OK]

Common Mistakes:

• Using average() which is not a MATLAB function
• Confusing sum() with average
• Using std() instead of mean()

3. What is the output of this MATLAB code?

A = [2, 4, 6, 8];
m = mean(A);
s = std(A);
disp([m, s]);

medium

A. [5 2.58199]

B. [4 2]

C. [6 3]

D. [5 3]

Solution

1. Step 1: Calculate the mean of A

   Mean = (2 + 4 + 6 + 8) / 4 = 20 / 4 = 5.

2. Step 2: Calculate the standard deviation of A

   Standard deviation ≈ 2.58199 for these values.

3. Final Answer:

   [5 2.58199] -> Option A

4. Quick Check:

   mean = 5, std ≈ 2.58 [OK]

Hint: Calculate mean and std separately, then display [OK]

Common Mistakes:

• Mixing up mean and std values
• Calculating sum instead of mean
• Using wrong formula for std

4. Find the error in this MATLAB code that tries to calculate the mean of B = [1, 3, 5, 7]:

B = [1, 3, 5, 7];
average = mean(B);
disp(average);

medium

A. mean() function is not defined in MATLAB

B. Missing semicolon after mean(B)

C. disp() cannot display variables

D. Variable name 'average' overwrites a function

Solution

1. Step 1: Check variable naming

   Using 'average' as a variable name is allowed but can confuse readers since it looks like a function name.

2. Step 2: Confirm syntax correctness

   There is no syntax error; semicolon is optional for suppressing output, mean() is a valid function, and disp() can display variables.

3. Final Answer:

   Variable name 'average' overwrites a function -> Option D

4. Quick Check:

   Variable name shadows function = C [OK]

Hint: Avoid naming variables same as functions [OK]

Common Mistakes:

• Thinking semicolon is mandatory
• Believing mean() is undefined
• Assuming disp() can't show variables

5. You have two data sets in MATLAB:

data1 = [10, 20, 30, 40];
data2 = [15, 25, 35, 45];

Which statistical tool helps decide if the difference between these sets is significant for decision making?

hard

A. t-test

B. std

C. sum

D. mean

Solution

1. Step 1: Understand the goal

   We want to check if the difference between two data sets is statistically significant.

2. Step 2: Identify the correct statistical test

   Mean and std show averages and spread but do not test significance. The t-test compares means to check significance.

3. Final Answer:

   t-test -> Option A

4. Quick Check:

   Significance test = t-test [OK]

Hint: Use t-test to compare two data sets statistically [OK]

Common Mistakes:

• Using mean or std to test significance
• Confusing sum with statistical tests
• Ignoring the need for a significance test