To calculate an average, add the values and divide by how many values you added. For 12, 15 and 18, the total is 45 and the count is three, so the average is 15. This familiar calculation is the arithmetic mean.
The arithmetic is usually straightforward. The more important question is what belongs in the list: every day or only active days, every measurement or one summary per group? A correct calculation can answer the wrong question if the count does not match the total.
Calculate the mean in three steps
Suppose five grocery trips cost $24, $31, $27, $38 and $30. These invented figures illustrate the calculation, rather than typical grocery spending. First, add all five amounts: 24 + 31 + 27 + 38 + 30 = 150. Next, count the trips: five. Finally, divide 150 by 5. The mean is $30 per trip.
Write the unit alongside the answer. An average cost per trip is different from an average cost per week. If those five trips happened across two weeks, spending averaged $75 per week, even though it averaged $30 per trip. The numerator stays $150; the denominator changes because the question changes.
Use the same unit for every entry. Convert hours and minutes into minutes before averaging durations. For example, 1 hour 20 minutes and 40 minutes become 80 and 40 minutes. Their average is 60 minutes, or one hour. Writing the first duration as 1.20 decimal hours would give the wrong input.
Mean, median and mode answer different questions
The mean shares the total equally across all observations. The median locates the middle observation after sorting. The mode identifies the most frequent value. These are standard measures of location described in the NIST statistics handbook.
Consider five waiting times: 4, 5, 5, 6 and 30 minutes. Their total is 50 minutes, so the mean is 10 minutes. The median is 5 because that is the third value in the ordered list. The mode is also 5 because it appears twice, more often than any other value.
With an even number of observations, average the two central values to find the median. For 4, 5, 6 and 30, the middle pair is 5 and 6, making the median 5.5 minutes. A list can have several equally frequent modes; if nothing repeats, there is no useful standout most-common value.
What to do when one value is unusually large
In the waiting-time example, four waits are six minutes or less, yet the mean is ten minutes. The 30-minute wait pulls it upward. The median better describes the middle experience here, while the mean still correctly accounts for all 50 minutes of waiting.
Check an unusual observation for a typo, a unit mismatch or a different situation. Do not delete it merely because it makes the result inconvenient. If it really happened and belongs to the question, keep it. Reporting both mean and median can show the difference between the overall total per observation and the middle experience.
A single average also hides spread. Lists of 9, 10, 11 and 0, 10, 20 both average 10, but the second varies much more. Include the smallest and largest values when that variation matters. An average alone cannot promise what the next observation will be.
Include genuine zeros; identify missing values
A zero is an observation. A blank may mean an observation was never recorded. Suppose a four-day reading log shows 20 minutes, 0 minutes, 30 minutes and one missing entry. Across the three recorded days, the mean is 50 ÷ 3, or about 16.7 minutes. You cannot claim a complete four-day mean from those records.
If you confirm that the missing day also involved no reading, enter another zero. Now the average is 50 ÷ 4 = 12.5 minutes per day. If you instead average only days with reading, you get 25 minutes per active day. Each result needs its matching description.
In Excel, =AVERAGE(A1:A4) includes numeric zeros but ignores empty cells in that range, as Microsoft documents. Check whether blanks mean unknown, not applicable or genuinely zero before trusting the result. Software cannot make that decision for you.
Combine groups using their sizes
Do not usually average two averages when they represent different numbers of observations. Imagine two small parcels averaging 4 kilograms each and six other parcels averaging 3 kilograms each. The first group totals 8 kilograms and the second totals 18. Together, 26 kilograms divided by eight parcels gives 3.25 kilograms per parcel.
Simply averaging 4 and 3 gives 3.5, which assigns the two-parcel group as much influence as the six-parcel group. To combine group means, multiply each mean by its group count, add those products, then divide by the combined count. If the supplied group means were rounded, the combined result is approximate too.
School calculations may use assigned percentages or course credits as weights rather than headcounts. See our guides to weighted assignment grades and GPA using credits and grade points for those specific rules.
Check the answer before you use it
You need at least one recorded numeric value; an empty list has no arithmetic mean. For an ordinary arithmetic mean, the result must lie between the smallest and largest inputs, including the endpoints. Multiply your unrounded mean by the number of observations: it should recover the total. A result outside the input range signals a mistake in the calculation or the entries.
Count repeated observations separately. Three days of 10 minutes and one day of 30 minutes average 15 minutes, not 20. Keep full precision during the calculation, then round the final answer to a useful level. Finally, label the result with its unit, observation count and any excluded or missing entries.
A basic calculator is enough for short lists. If you prefer physical keys, you can browse basic desktop calculators on Amazon. A phone calculator or spreadsheet works too.
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