Average Calculator

How to use the average calculator

Choose Mean, median, mode and paste or type your numbers, separated by commas, spaces or new lines. The calculator sorts them, finds every common type of average and shows the working. Choose Weighted average when some values count more than others: enter one value and its weight per line, such as 90, 30. Weights can be percentages, credit hours, quantities or any positive numbers, and they don’t have to add up to 100.

Average formulas

• Mean (arithmetic average) = sum of values ÷ number of values
• Median = the middle value of the sorted list. With an even count, it is the average of the two middle values.
• Mode = the value that occurs most often. A list can have one mode, several, or none.
• Range = largest value − smallest value
• Weighted average = Σ(value × weight) ÷ Σ(weight)
• Geometric mean = the nth root of the product of n values (all must be positive)
• Harmonic mean = n ÷ (sum of the reciprocals 1/x)

Worked example: test scores

Eight test scores: 85, 92, 78, 92, 88, 95, 70 and 80.

1. Mean: the sum is 680, and 680 ÷ 8 = 85.
2. Median: sorted, the scores are 70, 78, 80, 85, 88, 92, 92, 95. The middle two are 85 and 88, so the median is 86.5.
3. Mode: 92 appears twice and every other score once, so the mode is 92.
4. Range: 95 − 70 = 25.
5. Geometric mean: 84.61, and harmonic mean: 84.21. Both sit slightly below the arithmetic mean, as they always do when the values differ.

The median is a little above the mean here because one low score, 70, pulls the mean down more than it moves the middle of the list.

Weighted average for grades

When parts of a course count differently, a plain average gives the wrong grade. Suppose homework is worth 30%, tests 50% and the final exam 20%, and you scored 90, 82 and 75:

Part	Score	Weight	Score × weight
Homework	90	30	2,700
Tests	82	50	4,100
Final exam	75	20	1,500
Total		100	8,300

The weighted average is 8,300 ÷ 100 = 83. A simple average of the three scores would be 82.33, which undercounts the heavily weighted tests. The same method works for GPA with credit hours as weights; the GPA calculator handles letter grades for you, and the grade calculator works out what you need on the final.

Average price of shares (stock averaging)

Investors often buy the same stock at different prices and need the average cost. This is a weighted average, with the number of shares as the weight. Buy 100 shares at 250 and another 50 at 220 and you have paid 25,000 + 11,000 = 36,000 for 150 shares. The average price is 36,000 ÷ 150 = 240. The simple average of 250 and 220 is 235, which is wrong because you bought twice as many shares at the higher price. Enter 250, 100 and 220, 50 on two lines in weighted mode to check your own trades.

Which average should you use?

• Mean works well for symmetric data without extreme values, such as test scores or daily temperatures.
• Median is better for skewed data. Five salaries of 30, 32, 35, 38 and 200 thousand have a mean of 67 thousand but a median of 35 thousand, which describes a typical person far better.
• Mode is the only average for categories, such as the most common shoe size sold.
• Geometric mean is right for growth rates. An investment that gains 50% one year and loses 50% the next turns 100 into 150 and then 75. The arithmetic mean of the returns is 0%, but the geometric mean of the growth factors 1.5 and 0.5 is 0.866, a loss of about 13.4% a year. The CAGR calculator applies this to investments.
• Harmonic mean is right for averaging rates over the same distance, such as speeds. Driving one way at 60 km/h and back at 40 km/h averages 48 km/h.

Tips for accurate averages

• Check for typing errors first. A misplaced decimal point (8.5 instead of 85) drags the mean far more than the median.
• Use a dot for decimals. A comma separates values, so 2,5 is read as two numbers.
• Report the median alongside the mean when the data are skewed or contain outliers.
• To see how spread out the values are, not just their center, use the standard deviation calculator.