Say what you expect before you flip. Three quick rounds of coins, then the same idea on real heights.
Say how many heads you expect. Flip ten coins. See how close you were. Three times.
On the right, say how many heads you expect. Then flip until you've flipped ten. Three rounds — the tally tracks how close you were each time.
Expecting 5 counts as ✓ only when exactly 5 heads come up — about 1 round in 4. Even when a round comes up ✗, watch what happens to your three numbers.
How many heads do you expect to see in ten coin flips?
set.seed(42)flips <- rbinom(10, size = 1, prob = 0.5)sum(flips) # count of heads
How far off each round's prediction was from the actual heads count.
| Round | You expected | Heads that came up | Off by |
|---|
Across all 30 flips: you expected — heads in total, and — actually came up.
That last column — how far off each round was — is your error.
Add the three up. Your total error across the rounds: — heads (an average of — per round).
Now suppose you had expected 5 every single round — the middle of 0 to 10 — and never changed your mind. Your total error would have been — heads.
One number, used every round, against your three separate calls. Which came out closer — and why might the middle beat trying to read each round?
Real adult heights. Pick one number, then draw people until it fits.
Pick one height (in centimeters) you expect for a random adult. Click Draw to pull one, and repeat. If your average error across 30 draws lands close to zero, you move on. If not, you pick a new number and try again.
# 30 random adult heights from real data.nh <- read.csv("data/clean/nhanes_adults.csv")set.seed(7)truths <- sample(nh$Height, 30)guess <- ___ # type a value; aim for an average error near zeromean(guess - truths)
One number rarely fits everyone. Aim one at each group and watch what happens.
Same as Stage B, but the adults now come from two groups — women and men. Pick one height you expect for each. Then draw people from both and watch your two average errors, and how far apart the two crowds sit.
You are about to aim one number at each group. Before you start — which do you think will be larger?
Draw enough from both groups, then read the two numbers above. Which is bigger — the distance between the crowds, or the scatter inside one of them? What would that tell you about whether "women" and "men" are really one crowd or two?
# One number won't fit two groups.nh <- read.csv("data/clean/nhanes_adults.csv")women <- nh$Height[nh$Gender == "female"]men <- nh$Height[nh$Gender == "male"]expect_women <- ___expect_men <- ___abs(mean(men) - mean(women)) # gap between groupsmean(c(sd(men), sd(women))) # spread within a group