Descriptive statistics (mean, median, std) in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the mean in descriptive statistics?

The mean is the average value of a data set. You add all numbers and divide by how many numbers there are.

beginner

How do you find the median of a data set?

The median is the middle value when the data is sorted from smallest to largest. If there is an even number of values, it is the average of the two middle numbers.

beginner

What does the standard deviation (std) tell us about data?

Standard deviation shows how spread out the numbers are from the mean. A small std means data points are close to the mean; a large std means they are spread out.

beginner

MATLAB function to calculate the mean of an array?

Use the function mean(array) to get the average value of the numbers in the array.

beginner

How to calculate the standard deviation in MATLAB?

Use std(array) to find the standard deviation of the numbers in the array.

Which MATLAB function gives the middle value of a sorted data set?

A mean()

B median()

C std()

D sum()

The median() function returns the middle value of the data.

What does a high standard deviation mean?

A Data points are close to the mean

B Mean is zero

C Data points are spread out from the mean

D Data points are all the same

A high standard deviation means data points are spread out from the mean.

How do you calculate the mean in MATLAB?

A mean(array)

B median(array)

C std(array)

D sum(array)

The mean(array) function calculates the average.

If a data set has an even number of values, how is the median found?

A Average of the two middle values

B The smallest value

C The largest value

D The mean of all values

For even number of values, median is the average of the two middle values.

Which statistic measures the average value of data?

A Range

B Median

C Standard deviation

D Mean

The mean measures the average value.

Explain how to calculate mean, median, and standard deviation using MATLAB functions.

Think about the MATLAB functions that directly compute these statistics.

Describe what the standard deviation tells us about a data set and why it is useful.

Consider how data points differ from the average.

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