what is the third quartile for the following distribution of returns? 8% 10% 12% 13% 15% 17% 17% 18% 19% 23% 24% 26% L y = (12+1)x(75/100)=9.75 Third quartile is thus 19 + .75 x (23-19) = 22% Why is this? Why is the answer not simply 23%? After all, 9 data points out of 12, or 75% of the data points, lie below 23%. Isn’t 23% thus the third quartile?
it is the 9.75 th element. that is why you are doing a linear interpolation between the 9th and 10th term.
why the 9.75th? 9 out of 12 is already .75.
You typed your own answer in your question. You calculated the 9.75th element… N x .75 is 9, but here you are using (n+1) x .75 = 9.75
You typed your own answer in your question. You calculated the 9.75th element… N x .75 is 9, but here you are using (n+1) x .75 = 9.75.
to jmuch85, thanks - i see that you are citing the formula when you write (n+1) x .75 = 9.75, but i don’t understand where this formula is coming from?
Usual formula Decile = (n+1) * .1 Quantile = (n+1) * .25 3rd Quartile = (n+1) * .25 * 3 = (n+1) * .75 This is in the text definitely.
(12+1)*.25*3=9.75 19+ .75(23-19) = 22%