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Average Calculator

Compute mean, median, mode, and weighted averages instantly

Arithmetic Mean

30.00

Median

30.00

Count

5

Sum

150.00

Separate numbers with commas or spaces

Must have the same number of weights as data values. Leave empty for equal weights.

Arithmetic Mean

30

All Average Types

Median

30

Mode

None

Geometric Mean

26.0517

Harmonic Mean

21.8978

Summary Statistics

Count5
Sum150
Min10
Max50
Range40

Sorted Data

10, 20, 30, 40, 50

Formulas Used

Arithmetic Mean

μ = Σxᵢ / n

Sum all values and divide by the count. The most commonly used average.

Where:

μ= The arithmetic mean (population) or x̄ (sample)
xᵢ= Each individual value in the data set
n= The total number of values

Geometric Mean

GM = (x₁ × x₂ × ... × xₙ)^(1/n)

The nth root of the product of all values. Used for multiplicative quantities like growth rates.

Where:

GM= The geometric mean
xᵢ= Each value (must be positive)
n= The total number of values

Harmonic Mean

HM = n / Σ(1/xᵢ)

The reciprocal of the arithmetic mean of the reciprocals. Ideal for averaging rates.

Where:

HM= The harmonic mean
xᵢ= Each value (must be positive)
n= The total number of values

Example Calculations

1Average of Test Scores

Inputs

Numbers85, 92, 78, 95, 88

Result

Arithmetic Mean87.6
Median88
Min78
Max95
Range17

Sum = 85 + 92 + 78 + 95 + 88 = 438. Mean = 438 / 5 = 87.6. Sorted: {78, 85, 88, 92, 95}, so median = 88 (middle value). No mode since all values are unique.

2Weighted GPA Calculation

Inputs

Grades4.0, 3.0, 3.7, 2.7
Credits4, 3, 3, 2

Result

Weighted Average3.475

Weighted sum = 4.0×4 + 3.0×3 + 3.7×3 + 2.7×2 = 16 + 9 + 11.1 + 5.4 = 41.5. Total credits = 12. Weighted GPA = 41.5 / 12 = 3.4583.

3Average Growth Rates

Inputs

Numbers1.10, 1.20, 0.95, 1.15

Result

Geometric Mean1.0957
Arithmetic Mean1.1

Product = 1.10 × 1.20 × 0.95 × 1.15 = 1.4421. Geometric mean = 1.4421^(1/4) = 1.0957. This represents the true average growth multiplier across 4 periods.

Frequently Asked Questions

Q

What is the difference between mean, median, and mode?

Mean is the sum divided by the count. Median is the middle value when data is sorted. Mode is the most frequently occurring value. For the data set {2, 3, 3, 5, 7}: mean = 4, median = 3, mode = 3.

  • Mean (arithmetic): sum of all values divided by count
  • Median: middle value (or average of two middle values)
  • Mode: most frequently occurring value(s)
  • Skewed data: mean is pulled toward outliers, median is not
  • Multiple modes possible (bimodal, multimodal)
MeasureFormulaBest For
MeanΣx / nSymmetric data without outliers
MedianMiddle valueSkewed data or with outliers
ModeMost frequentCategorical data
Q

When should I use a weighted average?

Use a weighted average when some values contribute more than others. Common examples include calculating GPA (courses have different credit hours), portfolio returns (different investment sizes), and grading systems (exams worth more than homework).

  • GPA: 4-credit A (4.0) + 2-credit B (3.0) = (16+6)/6 = 3.67
  • Portfolio: weight by investment amount, not equal shares
  • Grades: final exam 40%, midterm 30%, homework 30%
  • Formula: Σ(wᵢ × xᵢ) / Σ(wᵢ)
ScenarioWeightsResult
Equal weights (3 items)1, 1, 1Same as arithmetic mean
GPA (4cr A, 2cr B)4, 23.67
Grades (90 hw, 80 exam)30%, 70%83
Q

What is the geometric mean and when is it used?

The geometric mean is the nth root of the product of n values. It is used for growth rates, ratios, and percentage changes. For returns of +10% and +20%: geometric mean = √(1.1 × 1.2) = 1.1489, or about 14.89% average return.

  • Formula: (x₁ × x₂ × ... × xₙ)^(1/n)
  • Used for: investment returns, population growth rates
  • Always ≤ arithmetic mean (AM-GM inequality)
  • Only works with positive numbers
  • For {4, 9}: geometric = √36 = 6 vs arithmetic = 6.5
Data SetArithmetic MeanGeometric Mean
2, 854
1, 10050.510
4, 4, 444
3, 12, 271410.9
Q

What is the harmonic mean and when should I use it?

The harmonic mean is n divided by the sum of reciprocals: n / Σ(1/xᵢ). It is ideal for averaging rates, speeds, or ratios. If you drive 60 mph for one leg and 40 mph for the return, the harmonic mean speed is 48 mph, not 50.

  • Formula: n / (1/x₁ + 1/x₂ + ... + 1/xₙ)
  • Use for: averaging speeds, rates, price-to-earnings ratios
  • Always ≤ geometric mean ≤ arithmetic mean
  • Only works with positive numbers
  • For equal-distance travel at 60 and 40 mph: HM = 48
DataArithmeticGeometricHarmonic
40, 605048.9948
2, 8543.2
1, 4, 432.522
Q

How do I calculate the median for an even number of values?

When you have an even count of values, the median is the average of the two middle values. Sort the data, find positions n/2 and n/2 + 1, and average them. For {3, 5, 7, 9}: median = (5 + 7) / 2 = 6.

  • Odd count: median is the exact middle value
  • Even count: average of the two middle values
  • Example (odd): {1, 3, 5, 7, 9} → median = 5
  • Example (even): {1, 3, 5, 7} → median = (3+5)/2 = 4
  • Always sort the data first
Data SetCountMiddle ValuesMedian
1, 2, 3, 4, 55 (odd)33
1, 2, 3, 44 (even)2, 32.5
10, 20, 30, 40, 50, 606 (even)30, 4035

Understanding Different Types of Averages

1

Arithmetic Mean vs. Median: When Each One Lies

The arithmetic mean (sum ÷ count) and the median (middle value) give identical results for symmetric data, but diverge dramatically with skewed distributions. The mean US household income in 2023 was approximately $114,000, while the median was $74,580 — a 53% difference caused by a small number of very high earners pulling the mean upward. In this case, the median is the more representative "average" because it is not distorted by outliers.

As a rule of thumb: use the mean for symmetric data without extreme values (test scores, temperatures, manufacturing measurements) and the median for skewed data or data with outliers (income, home prices, response times). The mode — the most frequently occurring value — is useful primarily for categorical data (most common shoe size, most popular color choice). This calculator computes all three simultaneously so you can compare and choose the most appropriate measure.

When to use each measure of central tendency
MeasureFormulaAffected by Outliers?Best Use Case
Arithmetic MeanΣx / nYes, heavilySymmetric, continuous data
MedianMiddle valueNoSkewed data, income, prices
ModeMost frequentNoCategorical data, surveys
2

Weighted Average: GPA, Portfolios, and Grading

A weighted average assigns different importance to different values, reflecting real-world situations where not all data points contribute equally. The formula is Σ(wᵢ × xᵢ) / Σ(wᵢ). For GPA calculation: a 4-credit A (4.0) and a 2-credit B (3.0) produces (4 × 4.0 + 2 × 3.0) / (4 + 2) = 22/6 = 3.67, not the simple average of 3.5.

Investment portfolio returns work the same way. If 70% of your portfolio returns 8% and 30% returns 12%, the weighted return is (0.70 × 8 + 0.30 × 12) = 9.2%, not the simple average of 10%. Grade calculations often use weights: if the final exam is 40%, midterm 30%, and homework 30%, a student scoring 90 on homework, 80 on the midterm, and 85 on the final earns (0.30 × 90 + 0.30 × 80 + 0.40 × 85) = 85.0 — not the simple average of 85.

When all weights are equal, the weighted average reduces to the arithmetic mean. Unequal weights always pull the result toward the most heavily weighted values.

3

Geometric and Harmonic Means: Specialized Averages

The geometric mean is the nth root of the product of n values: GM = (x₁ × x₂ × ... × xₙ)^(1/n). It is the correct average for multiplicative quantities like investment returns and population growth rates. If an investment returns +50% year 1 and –33% year 2, the arithmetic mean suggests +8.5% average return, but the actual result is break-even: $100 → $150 → $100. The geometric mean correctly yields √(1.50 × 0.67) = 1.002, or approximately 0% — matching reality.

The harmonic mean is n divided by the sum of reciprocals: HM = n / Σ(1/xᵢ). It is the correct average for rates and speeds over equal distances. Driving 60 mph for 30 miles and 30 mph for 30 miles covers 60 miles in 1.5 hours = 40 mph average. The arithmetic mean (45 mph) would overestimate. The harmonic mean: 2 / (1/60 + 1/30) = 40 mph — matching reality. Use the harmonic mean whenever you average rates over fixed distances or quantities.

Comparison of three mean types (all equal when values are identical)
Data SetArithmetic MeanGeometric MeanHarmonic Mean
40, 605048.9948
1.5, 0.67 (returns)1.0851.0020.93
2, 8543.2
10, 10, 10101010

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Last Updated: Mar 26, 2026

This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.

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