Average Calculator

Math

Calculate arithmetic mean, weighted average, geometric mean, harmonic mean, median, mode, and target exam grade needed to reach a desired average score.

Presets:

Arithmetic Average (Mean)

25 (n = 7, sum = 175)

Central Tendencies & Pythagorean Means

Median 25

Mode No Mode

Range 30

Geometric Mean 22.7458

Harmonic Mean 20.3742

RMS (Quadratic Mean) 26.9258

Smallest: 10 Largest: 40 Total Sum: 175

Step-by-Step Calculation Working

1 1. Count and Summation

n = 7, ∑x = 10 + 15 + 20 + 25 + 30 + 35 + 40 = 175

Total count of observations and sum of all numerical values in the dataset.

2 2. Arithmetic Mean (Average)

x̄ = (∑x) / n = 175 / 7 = 25

The central value obtained by dividing the sum of values by the number of values.

3 3. Median (Middle Value)

Sorted = [10, 15, 20, 25, 30, 35, 40] → Median = 25

Middle value of the sorted sequence.

4 4. Pythagorean & RMS Means

Geometric Mean: 22.7458 | Harmonic Mean: 20.3742 | RMS: 26.9258

Specialized averages: Geometric for growth rates, Harmonic for rates/ratios, RMS for magnitudes/signals.

How This Calculator Works

An average represents the central tendency of a group of numbers. While the standard arithmetic mean is the most common, different mathematical averages are suited to specific real-world problems: weighted averages for grades and credit hours, geometric means for investment returns, and harmonic means for rates and speed.

📐 Mathematical Formulas for Different Types of Averages

Arithmetic: x̄ = ∑x / n | Weighted: x̄_w = ∑(w · x) / ∑w | Geometric: (∏x)^(1/n)

Arithmetic Mean: Standard average calculated by summing all values and dividing by the count n

Weighted Average: Accounts for the varying relative importance or credit weights of each data point

Geometric Mean: nth root of the product; essential for compound interest and multiplicative growth

Harmonic Mean: Reciprocal of the arithmetic mean of reciprocals; ideal for speeds, densities, and P/E ratios

Root Mean Square (RMS): Square root of mean squares; used in engineering and physics for alternating currents

Key Mathematical Rules & Properties

Simple Average Calculation

Add up all numbers in the dataset and divide by the total number of items.

Weighted Average Calculation

Multiply each score by its corresponding weight, sum the products, and divide by total weight.

Target Grade Calculation

Subtract currently earned weighted points from total points needed, then divide by final exam weight.

Understanding your calculation

Method, example and limitations

How the calculation works

The arithmetic average is the sum of the entered observations divided by their count. A weighted average instead multiplies each observation by its weight before normalizing.

Example to check

The average of 10, 20 and 30 is 60 / 3 = 20.

Before using the result

Averaging percentages with different underlying totals can be misleading. Use suitable weights and check whether zero values are real observations or missing data.

Calculation methodology · Report a result that needs review