How to find mean, median, and mode

Why homework asks for all three

They answer different questions. Mean is the balance point. Median is a typical value that ignores how far the tails go. Mode is the most common category or number. A skewed salary list can have a mean far above the median.

Formulas and rules

Median: sort the data. If n is odd, take position (n+1)/2. If n is even, average the two central observations.

Mode: the most frequent value. A list can have no mode, one mode, or more than one mode.

Worked list

Data: 3, 7, 7, 8, 12. n = 5. Already sorted.

1. Mean = (3+7+7+8+12)/5 = 37/5 = 7.4.
2. Median = 7 (third value).
3. Mode = 7 (appears twice).

On iPhone

1. Open Statistics Problem Solver Pro → Calculators → Mean, Median, Mode.
2. Enter the numbers in the same order the homework gives, or sorted — order does not change these three once all values are included.
3. If the question is a word problem with a table in a photo, scan the table instead of typing.

Useful tips

• Count n twice. An off-by-one error in n moves the mean and the median position.
• For even n, the median is not a value that has to appear in the list.
• After the mean, spread is next: standard deviation.

Common mistakes

• Leaving the list unsorted and picking a “middle” that is not the median.
• Calling every repeated value a mode when one value clearly appears more often.
• Using the mean of a heavily skewed set as if it were typical, when the question asked for a resistant measure.

How Statistics Problem Solver Pro helps

Mean, median, and mode are the first calculators named on the App Store listing. They are free, offline, and do not use your three included AI solves. For a written solution with substitutions, scan the problem and expand each step.

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