Averages, Medians, and Spread

Rows of scouting data are useless until you summarize them. Two kinds of numbers do almost all the work: measures of center (where a team’s typical performance sits) and measures of spread (how much it bounces around).

Measures of Center

Mean (average): Add every value and divide by the count. For game pieces [4, 5, 6], the mean is (4+5+6)/3 = 5. In a sheet, =AVERAGE(C2:C50). The mean uses every data point, which makes it informative but also easy to skew.

Median: Sort the values and take the middle one. For [4, 5, 6] the median is 5. With an even count like [4, 5, 6, 9], average the two middle values: (5+6)/2 = 5.5. In a sheet, =MEDIAN(C2:C50).

Why the Median Resists Outliers

An outlier is a value far from the rest. Watch what one bad match does. Say a team scores [5, 6, 5, 6, 0] — that 0 was a dead battery, not their real ability.

• Mean = (5+6+5+6+0)/5 = 4.4
• Median = sort to [0, 5, 5, 6, 6], middle value = 5

The single 0 dragged the mean down more than half a point; the median barely moved. The median is resistant because it only cares about the middle value’s position, not how extreme the flukes are. The mean is not — every value pulls on it. When a team’s data is skewed by a breakdown or a no-show, the median tells the more honest story. When their matches are fairly even, the mean captures more.

Measures of Spread

Two teams can share an average and play nothing alike. Spread is how you measure consistency — and at FRC, a partner you can count on often beats a partner who might explode.

• Range = max minus min (=MAX(...)-MIN(...)). Easy, but one outlier blows it up.
• Standard deviation measures how far values typically fall from the mean. Small means tightly clustered and reliable; large means boom-or-bust. In a sheet, =STDEV(C2:C50).

A Worked Example

Two teams, five matches each, both averaging 6 game pieces:

1. Team A: [6, 6, 5, 7, 6] — mean 6, range 2, low standard deviation. Rock-solid.
2. Team B: [1, 11, 2, 10, 6] — mean 6, range 10, high standard deviation. A coin flip.

On average alone they look identical. Spread reveals Team A is a dependable second pick and Team B is a gamble you only take if you need a ceiling that high. In an elimination bracket where one dead match ends your day, that difference decides who you call.

So always report center and spread together. An average without spread is half the story — and the half that gets alliances knocked out early.

Key takeaways

• The mean uses every value but is pulled by outliers; the median is the middle value and resists them.
• Use the median when data is skewed or has extreme values (like a dead-battery zero); use the mean when data is fairly even.
• Range (max minus min) is quick but fragile; standard deviation measures typical distance from the mean and captures consistency.
• Two teams can share an average while differing wildly in spread, so always report center and spread together.
• In spreadsheets: =AVERAGE, =MEDIAN, =MAX-MIN for range, and =STDEV for standard deviation.

This lesson was adapted from learnfrc.com.