HexMathv1.0.3

Average calculator with steps

Enter the values you want to average. HexMath adds them, divides by the count and shows each step.

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What this page covers

  • The mean of a list of numbers, including negatives, decimals and fractions.
  • Weighted averages, where each value counts a given number of times or carries a weight.
  • Working backward to the missing value that gives a target average.
  • Not covered here: the middle value of a sorted list (use Median calculator) and how spread out the data are (use Standard deviation calculator).

How to enter the problem

  • Type find the average of, then the numbers separated by commas.
  • Scan it. Fit the one problem in the frame.
  • Choose a photo. Several problems in one photo are solved as a list.
  • Then tap Solve.

Worked examples

Example 1

Problem

Find the average of the quiz scores 78, 85, 92 and 88.

Answer

Verified

The answer is

85.7585.75

Explanation

  1. Add the values
    78+85+92+88=34378 + 85 + 92 + 88 = 343
  2. Count the values
    There are 4 scores.
  3. Divide the total by the count
    3434=85.75\frac{343}{4} = 85.75

Example 2

Problem

A student scores 90 on 3 tests, 80 on 4 tests and 70 on 2 tests. Find the average over all 9 tests.

Answer

Verified

The answer is

7309≈81.11\frac{730}{9} \approx 81.11

Explanation

  1. Multiply each score by how often it occurs
    3⋅90=2703 \cdot 90 = 270, 4⋅80=3204 \cdot 80 = 320, 2⋅70=1402 \cdot 70 = 140.
  2. Add the products
    270+320+140=730270 + 320 + 140 = 730
  3. Divide by the total count
    3+4+2=93 + 4 + 2 = 9 tests, so the average is 7309\frac{730}{9}.
  4. Round at the end
    7309≈81.11\frac{730}{9} \approx 81.11.

Example 3

Problem

The average of five numbers is 80. The known ones are 72, 85, 90 and 78. Find the missing number.

Answer

Verified

The answer is

x=75x = 75

Explanation

  1. Find the total the average requires
    Five numbers with average 80 add to 5⋅80=4005 \cdot 80 = 400.
  2. Add the known numbers
    72+85+90+78=32572 + 85 + 90 + 78 = 325
  3. Subtract
    The missing number is 400−325=75400 - 325 = 75.
  4. Check
    325+755=4005=80\frac{325 + 75}{5} = \frac{400}{5} = 80

Common mistakes

  • Dividing by the wrong count, for example leaving out a value of 0. A zero still counts as one of the values.
  • Averaging the averages. In worked example 2, the plain average of 90, 80 and 70 is 80, but each score occurs a different number of times, so the true average is 7309\frac{730}{9}.
  • Rounding the values or the total before dividing. Round only the final answer.

Checks, assumptions and limits

  • Check that the answer lies between the smallest and largest values. For the runnable example, 16 is between 9 and 22.
  • Check by multiplying back: the average times the count gives the total. 16⋅5=80=12+17+9+20+2216 \cdot 5 = 80 = 12 + 17 + 9 + 20 + 22.
  • Average here means the arithmetic mean. The median is another kind of average, with its own page.
  • HexMath can make mistakes. Double check important steps.

Related tasks

Frequently asked questions

In everyday use, yes. The average usually means the arithmetic mean: the total divided by the number of values. Some classes also call the median and the mode averages, so check which one the question asks for.

Multiply each value by its weight, add the products, and divide by the sum of the weights. When the weights are percentages that add up to 100 percent, dividing by the sum of the weights means dividing by 100.

Yes. Use the camera on the one problem, or choose a photo. Several problems in one photo are solved as a list.

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