How to find the lower an upper quartile given an even set of

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!

Solution

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.

Ans.:-

1) Lower Quartile Q1 = 1.5

2) Upper Quartile Q3 = 4.5