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Sagot :
You have the distances traveled by n=15 empoyees to their workplace
9, 37, 24, 3, 13, 7, 18, 5, 32, 1, 18, 6, 22, 15, 28
To calculate the percentiles you'll need to have the data ordered from least to greatest
1, 3, 5, 6, 7, 9, 13, 15, 18, 18, 22, 24, 28, 32, 37
a) The 20th percentile separates the bottom 20% of the sample from the top 80%
You have to calculate its position by multipliyin the total number of observations by 0.20
15*0.2= 3
This means that the 20th percentile corresponds to the 3rd observation:
1, 3, 5, 6, 7, 9, 13, 15, 18, 18, 22, 24, 28, 32, 37
P₂₀= 5 miles
b) The 75th percentile separates the bottom 75% of the observations from the top 25%
As before, you have to calculate its position by multiplying the total ob observations by 0.75
15*0.75=11.25
The 75th percentil is between positions 11 and 12, you have to determine both positions then average them
1, 3, 5, 6, 7, 9, 13, 15, 18, 18, (22), (24), 28, 32, 37
Position 11: 22
Position 12: 24
Now calculate the average value between both positions:
(22+24)/2= 23
P₇₅= 23 miles
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