Percentiles

A percentile is the percentage of observations that fall below a given datapoint.

Graphically, percentile is the area below the probability distribution curve to the left of that observation.

# A graph of the SAT distribution
function signifChop(num, digits)
    if num == 0.0 then
        return num
    else
        e = ceil(log10(abs(num)))
        scale = 10^(digits - e)
        return trunc(num * scale) / scale
    end
end


𝜇=1500
𝜎=300
using Rmath
percentile = signifChop(pnorm(1800,𝜇,𝜎)*100,3)
plot(Normal(𝜇,𝜎), title="Normal Distribution N($(𝜇),$(𝜎)) to $(percentile) percentile", lw=3, label=["SAT Distribution"], fillrange=0)
xlims!((0,1800))

svg

# We can calculate percentiles with R/Julia:
pnorm(1800,𝜇,𝜎)
0.8413447460685429