Question

Here is the results of ten observations. 0, 7, 9, 14, 33, 0, 5, 8, 12, 22 a) Calculate the 25th percentile b) calculate the 75th percentile c) calculate the 50th percentile

Answer 1

we have the formula percentile = value

where i is the percentile number and N is the total number of observations

we have N = 10

first, we need to arrange the data in ascending order

0,0,5,7,8,9,12,14,22,33

(1) 25th percentile, we have i = 25, N= 10

so, 25th percentile = (25*10)/100 = 250/100 = 2.5th value

but there is no 2.5th value, so we will take the average of 2nd and 3rd values

this gives, average = (0+5)/2 = 5/2 = 2.5

So, 25th percentile = 2.5

(b) 75th percentile, we have i = 75, N= 10

so, 25th percentile = (75*10)/100 = 750/100 = 7.5th value

but there is no 7.5th value, so we will take the average of 7th and 8th values

this gives, average = (12+14)/2 = 26/2 = 13

So, 75th percentile = 13

(c) 50th percentile, we have i = 50, N= 10

so, 50th percentile = (50*10)/100 = 500/100 = 5th value

So, 50th percentile = 8