Question 1

What is the difference between mean, median, and mode

Accepted Answer

Mean: Arithmetic average (sum ÷ count) Median: Middle value when sorted Mode: Most frequent value

Example: Data set 2, 3, 3, 5, 7

Mean: 4
Median: 3
Mode: 3

Question 2

How do I calculate the average of percentages

Accepted Answer

Same as regular average:

Mean = (Percentage 1 + Percentage 2 + ...) / Count

Example: Test scores 85%, 92%, 78%

Mean = (85 + 92 + 78) / 3 = 255 / 3 = 85%

For weighted percentages: Use weighted average formula

Weighted Mean = Σ(Percentage × Weight) / ΣWeights

Question 3

Why is the median different from the mean

Accepted Answer

When data is symmetrical: Mean ≈ Median When data is skewed: Mean ≠ Median

Skewed right (positive skew): Mean > Median

Example: Income (few billionaires skew mean up)

Skewed left (negative skew): Mean < Median

Example: Test scores (few very low scores)

Question 4

What if there is no mode

Accepted Answer

No mode occurs when:

All values appear only once
All values appear equally often

Examples:

1, 2, 3, 4, 5 → No mode
1, 1, 2, 2, 3, 3 → No mode (all appear twice)

What to do:

Report "no mode"
Use mean or median instead
For bimodal data, report both modes

Question 5

How do I calculate a weighted average

Accepted Answer

Formula:

Weighted Mean = Σ(Value × Weight) / ΣWeights

Example: Grade calculation

Test 1: 85% (20% weight)
Test 2: 90% (30% weight)
Final: 88% (50% weight)

Weighted Mean = (85 × 0.20 + 90 × 0.30 + 88 × 0.50) / 1
Weighted Mean = (17 + 27 + 44) / 1 = 88%

Question 6

What is a moving average

Accepted Answer

Average of most recent N data points:

Used for:

Stock prices
Weather trends
Sales data
Time series analysis

Calculation:

Moving Average = Sum of last N values / N

Example: 3-day moving average

Day 1-3: (10 + 12 + 15) / 3 = 12.33
Day 2-4: (12 + 15 + 11) / 3 = 12.67
Day 3-5: (15 + 11 + 14) / 3 = 13.33

Question 7

How do outliers affect the average

Accepted Answer

Mean: Highly sensitive to outliers

One extreme value significantly changes mean

Median: Resistant to outliers

Extreme values have minimal effect

Example: Data set 1, 2, 3, 4, 5

Mean: 3
Median: 3

Add outlier 100: 1, 2, 3, 4, 5, 100

Mean: 19.17 (changed dramatically)
Median: 3.5 (barely changed)

Question 8

Can I average averages

Accepted Answer

Generally NO unless:

Sample sizes are equal
Or you weight by sample size

Example (WRONG):

Class A: 20 students, mean 80%
Class B: 30 students, mean 90%
Incorrect mean of means: (80 + 90) / 2 = 85%

Correct (weighted):

Mean = (80 × 20 + 90 × 30) / (20 + 30)
Mean = (1,600 + 2,700) / 50 = 86%

Question 9

What is the difference between average and weighted average

Accepted Answer

Simple average: All values count equally

Mean = ΣValues / N

Weighted average: Some values count more

Weighted Mean = Σ(Value × Weight) / ΣWeights

Example:

Grades: 85, 90, 88 (simple average: 87.67)
With weights (20%, 30%, 50%): 88%

Question 10

How do I calculate the range

Accepted Answer

Simple formula:

Range = Maximum value - Minimum value

Example: 5, 12, 18, 25, 30

Range = 30 - 5 = 25

Coefficient of Range:

Coefficient = (Max - Min) / (Max + Min)

Normalizes range to 0-1 scale for comparison.

Practice Problems

Question 11

Problem 1: Calculate Mean, Median, Mode

Accepted Answer

Data set: 15, 22, 18, 25, 22, 30, 22, 28

Tasks: a) Calculate mean b) Calculate median c) Calculate mode d) Calculate range

Solution:

a) Mean:

Sum = 15 + 22 + 18 + 25 + 22 + 30 + 22 + 28 = 182
Mean = 182 / 8 = 22.75

b) Median: Sorted: 15, 18, 22, 22, 22, 25, 28, 30 Middle values: 22 and 22

Median = (22 + 22) / 2 = 22

c) Mode: 22 appears 3 times (most frequent)

Mode = 22

d) Range:

Range = 30 - 15 = 15

Question 12

Problem 2: Weighted Average

Accepted Answer

Scenario: Calculate final grade

Components:

Homework: 88% (weight 15%)
Quizzes: 92% (weight 25%)
Midterm: 85% (weight 30%)
Final: ? (weight 30%)

Target grade: 90%

Task: What score needed on final?

Solution:

Current points = 88 × 0.15 + 92 × 0.25 + 85 × 0.30
Current points = 13.2 + 23 + 25.5 = 61.7

Points needed for 90%: 90 - 61.7 = 28.3
Final needed: 28.3 / 0.30 = 94.33%

Need 94.33% on final (challenging but possible)

Question 13

Problem 3: Outlier Impact

Accepted Answer

Data set A: 10, 12, 15, 18, 20 Data set B: 10, 12, 15, 18, 100

Tasks: a) Calculate mean for both b) Calculate median for both c) Which measure is more affected by outlier?

Solution:

a) Mean:

Set A: (10 + 12 + 15 + 18 + 20) / 5 = 75 / 5 = 15
Set B: (10 + 12 + 15 + 18 + 100) / 5 = 155 / 5 = 31

b) Median:

Set A: 15 (middle value)
Set B: 15 (middle value)

c) Analysis:

Mean changed from 15 to 31 (doubled!)
Median stayed at 15 (no change)
Mean is more affected by outliers

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Conclusion

Understanding different types of averages and when to use each one is essential for data analysis, academic success, and informed decision-making. The mean provides the arithmetic average, the median gives the middle value resistant to outliers, the mode identifies the most frequent value, and the range measures variability.

Key takeaways:

Choose the right average for your data
- Mean: Normal distributions, no outliers
- Median: Skewed data, outliers present
- Mode: Categorical data, finding most common
- Range: Measuring spread
Understand your data distribution
- Check for outliers before calculating
- Determine if data is skewed
- Consider the context of your data
Use multiple measures together
- Compare mean and median to detect skew
- Report range with mean for context
- Use all measures for complete picture
Be aware of limitations
- Each measure has strengths and weaknesses
- No single measure tells the whole story
- Context matters for interpretation
Apply to real-world situations
- Business: Sales metrics, performance data
- Education: Grade analysis, test scores
- Science: Experimental data, research results
- Sports: Player and team statistics

Remember that statistics is a tool for understanding data, not an end in itself. Always consider the context of your data, the purpose of your analysis, and the audience for your results when choosing and interpreting averages.

Ready to analyze your data? Use our average calculator to find mean, median, mode, and range instantly!

Average Calculator - Calculate Mean, Median & Mode

Average Calculator

Types of Averages

Mean (Arithmetic Average)

Median

Mode

Range

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