01
The deviation strip
Teal = above reference, plum = below. Bar length = deviation.
Tip: press Enter to update · Shift+Enter for a new line
n–
Mean (x̄)–
Median (M)–
Mode–
Range–
above reference
below reference
±1σ band
M.D.
–
Variance σ²
–
Std. Dev. σ
–
Coeff. of Var.
–
| xᵢ | xᵢ − ref | |xᵢ − ref| | (xᵢ − ref)² |
|---|---|---|---|
| Σ | – | – | – |
Raw deviations sum to ≈0. |deviation| ÷ n = M.D. Squared deviation ÷ n = variance σ².
02
What happens as n grows
Watch mean, median, mode settle as n grows.
mean(n)
median(n)
mode(n)
current n
Mean at n
–
Median at n
–
Mode at n
–
S.D. at n
–
Try "Inject one outlier": mean jumps, median barely moves.
03
Step-deviation, grouped data
Edit classes and frequencies. Applies formula (12), Example 5.
Assumed mean A =
Class width h =
| Class | xᵢ (mid) | fᵢ | yᵢ | fᵢyᵢ | fᵢyᵢ² | |
|---|---|---|---|---|---|---|
| Total N | – | – | – | – | ||
Mean x̄
–
Mode
–
Variance σ²
–
Std. Dev. σ
–
Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)]×h, on the modal class.
04
Which one is more consistent?
Lower C.V. = more consistent, even with similar means (Example 6).
Factory A
Mean
–
S.D.
–
C.V.
–
Factory B
Mean
–
S.D.
–
C.V.
–
–