Average and Statistics
Statistics helps summarize, organize, and interpret data. Average and statistical measures are frequently tested in TU CMAT examinations to evaluate numerical reasoning and data analysis skills.
Practice MCQs for Average and Statistics
Fundamental Principles
Statistics
Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data.
Average
An average is a single value that represents a group of observations.
Arithmetic Mean
The sum of all observations divided by the total number of observations.
Median
The middle value of an ordered dataset.
Mode
The value that occurs most frequently in a dataset.
Range
The difference between the largest and smallest observations.
Frequency
The number of times a particular value occurs.
Weighted Average
An average where different observations contribute differently according to assigned weights.
Arithmetic Mean
Arithmetic Mean is the sum of all observations divided by the total number of observations. It is the most commonly used measure of central tendency.
Weighted Arithmetic Mean
Weighted Arithmetic Mean is an average in which each observation contributes according to its assigned weight or importance.
Quartiles
Quartiles divide an ordered dataset into four equal parts. Q1 is the first quartile, Q2 is the median, and Q3 is the third quartile.
Range
Range measures the spread of data and is calculated as the difference between the largest and smallest observation.
Essential Formulation Tips
- Use shortcut formulas whenever possible.
- For consecutive numbers, avoid adding all values manually.
- In average problems, think in terms of total sum.
- When a new value is added, update the total before recalculating the average.
- Convert word problems into average equations.
Shortcut Execution Techniques
- Total Sum = Average × Number of Items
- If average increases by x, total increases by x × number of items.
- Average of equally spaced numbers is the middle term.
- For consecutive integers, average lies exactly at the center.
- Use alligation concept for advanced weighted average questions.
Contextual Inquiries (FAQs)
Q: What is the most important average formula for CMAT?
A: Total Sum = Average × Number of Observations.
Q: When should median be used instead of mean?
A: When the dataset contains extreme values or outliers.
Q: Can a dataset have more than one mode?
A: Yes. Such datasets are called bimodal or multimodal.
Example Breakdown: Arithmetic Mean
Basic average calculation.Sum = 10 + 20 + 30 + 40 + 50 = 150
Number of observations = 5
Average = 150 ÷ 5 = 30
Example Breakdown: Combined Average
Frequently asked CMAT question.Total marks of first group = 20 × 60 = 1200
Total marks of second group = 30 × 70 = 2100
Combined average = (1200 + 2100) ÷ 50
Combined average = 66
Example Breakdown: Median
Basic median problem.Arrange data in ascending order
Middle value = 5
Median = 5
Example Breakdown: Mode
Basic mode problem.8 appears most frequently
Mode = 8
Example Breakdown: Average of Consecutive Numbers
Common CMAT shortcut question.Average = (First + Last) ÷ 2
Average = (11 + 21) ÷ 2
Average = 16
CMAT Average Basics Set 1
Fundamental average and arithmetic mean problems.
Q1. Find the average of 10, 20, 30, 40 and 50.
Q2. The average of 5 numbers is 12. What is their sum?
Q3. Find the average of 15, 25 and 35.
Q4. The average age of 4 students is 18 years. Total age is:
Q5. Average of first 5 natural numbers is:
Q6. Average of 8, 12, 16 is:
Q7. If average of 10 numbers is 15, their sum is:
Q8. Average of 5, 10, 15, 20 is:
Q9. Average is also known as:
Q10. Formula of average is: