step 1 step 215 original values now sorted

car speed (mph) car speed (mph)1 20 1 202 23 14 213 26 2 234 48 10 235 33 11 256 46 3 267 31 7 318 32 8 329 34 5 3310 23 9 3411 25 13 3712 48 6 4613 37 15 4714 21 4 4815 47 12 48

n (cars) 15 all datan*50% 7.5 50% of datan*85% 12.75 85% of data

as sorted

observation12 4613 47

interpolate what 12.75 would be

12.75 46.75

85%

of t

he c

ar o

bser

vatio

ns a

re 1

2.75

, w

hich

is b

etw

een

12 a

nd 1

3 ob

serv

ation

s

so THIS is your 85th percentile. It's not an actual value that you measured, but it is what it would be even when you have less than 85 measurements.

this value doesn't agree with what Excel calculates. I think this is because Excel does a better job of estimating percentiles than the rough linear interpolation I have done here.

You might think that if you have to determine an 85th percentile that this means you have to have 85 individual observations at minimum. This is not true. I am trying to demonstrate this with this example using only 15 speed measurement ranging 20-47 mph.

so THIS is your 85th percentile. It's not an actual value that you measured, but it is what it would be even when you have less than 85 measurements.

this value doesn't agree with what Excel calculates. I think this is because Excel does a better job of estimating percentiles than the rough linear interpolation I have done here.

step 3 (kind of optional)you can ask Excel to calculate percentiles that you want to show

percentiles speed (mph)1% 20.145% 20.710% 21.815% 2320% 2325% 2430% 25.235% 25.940% 2945% 31.350% 3255% 32.760% 33.465% 34.370% 36.475% 41.580% 46.285% 46.990% 47.695% 4899% 48

so THIS is your 85th percentile. It's not an actual value that you measured, but it is what it would be even when you have less than 85 measurements.

this value doesn't agree with what Excel calculates. I think this is because Excel does a better job of estimating percentiles than the rough linear interpolation I have done here.

15 20 25 30 35 40 45 500%

10%20%30%40%50%60%70%80%90%

100%

speed (mph)

perc

entil

es

You might think that if you have to determine an 85th percentile that this means you have to have 85 individual observations at minimum. This is not true. I am trying to demonstrate this with this example using only 15 speed measurement ranging 20-47 mph.

so THIS is your 85th percentile. It's not an actual value that you measured, but it is what it would be even when you have less than 85 measurements.

this value doesn't agree with what Excel calculates. I think this is because Excel does a better job of estimating percentiles than the rough linear interpolation I have done here.