Algebra, averages & word problems · Topic 8 of 15

Mean, Median, Mode & Range

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Math · averages

Mean is the sum divided by the count, median the middle value in order, mode the most frequent, range highest minus lowest.

01 · MeanMean = sum ÷ number of values

02 · MedianMedian = middle value, in order

03 · ModeMode = the most frequent value

Median = the middle value after ordering smallest to largest must know

Mode = the value that appears most often (85, 90, 85, 70, 95 → 85) must know

Outliers pull the mean, not the median (1, 2, 3, 4, 40: mean 10, median 3)

Even count: median = average of the two middle values

A set can have no mode or several modes

"Average" on its own means the mean

Missing value = (mean × count) − sum of the known values

Mean = sum of the values ÷ number of values must know

Range = highest value − lowest value (95 − 70 = 25) must know

72, 80, 76, 68, 84: 380 ÷ 5 = mean 76

4, 10, 6, 8 → 4, 6, 8, 10 → (6 + 8) ÷ 2 = 7

Need a mean of 85 on 4 tests after 80, 90, 82: 340 − 252 = 88

Commonly confused

	Mean	Median
How to find it	Add all values, divide by the count	Order the values, take the middle
Even number of values	Same method	Average the two middle values
An extreme value	Pulls it toward the outlier	Barely moves
1, 2, 3, 4, 40	50 ÷ 5 = 10	3

Sort before you find the median

Range is one number: 3 to 9 → range 6, not "3–9"

Show 2 more facts

One extreme value can inflate the range

The mean always falls between the lowest and highest values

Pearl

Median is the middle, so line the numbers up first.

Practice this topic, then test the whole section.

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