How to find the lower an upper quartile given an even set of data?Take 2, 2.5 ,4,5.5,6,7 as an example!
A little clarification:-
Ans:- Q1 = 2.5 & Q3 = 6
Quartiles are basically measures of central tendancy in a group of data that divide it in four subgroups by three quartiles Q1, Q2 and Q3.
Q1 - First Quartile - seperates first 1/4th data from remaining 3/4th data (located at 25th precentile)
Simillarly Q2 and Q3 are located 50th and 75th percentile.
Now, the formula for finding quartile is i = (P/100)*n where p = percentile and n = number of terms in data.
If we get i=whole number, we take the quartile as the average of ith term and (i+1)th from the data, eg. if i obtained is 3, we take average of 3rd and 4th term as quartile
If "i" obtained is not whole number, we simply take next term as quartile, eg. if i obtained is 3.75, we take 4th term as quartile.
In your example,
Date = 2, 2.5, 4, 5.5, 6, 7
Q1(Lower Quartile), p=25, n= 6
i = (25/100)*6 = 1.5,
Since i obtained is not a whole number, we take 2nd number as quartile, therefore Q1 = 2.5
Simillary for Q3(Upper Quartile), p=75, n=6
i = (75/100)*6 = 4.5
Since i obtained is not whole number, we take 5th number as quartile, therefore Q4 = 6.
1) Lower Quartile Q1 = 1.5
2) Upper Quartile Q3 = 4.5