# question on five number summary & quantile.

i know that in five number summary :

25% of a data set lies between Min & 1st quartile.

50% of a data set lies between Min & 2nd quartile, that is, Median.

75% of a data set lies between Min & 3rd quartile.

& 100% of a data set lies between Min & Max.

But my cocept is contradicting as i run a data set in R Programming Language.

while i wrote the command fivenum(x) & quantile(x) the percentiles are not matching that is, "the 1st quartile of fivenum(x)" is not "the the value below which 25% of the data fall in quantile(x)"

the commands that i have run in R console:

y <- c(7,12,9,1)

fivenum(y)

[1] 1.0 4.0 8.0 10.5 12.0

quantile(y)

0% 25% 50% 75% 100%

1.00 5.50 8.00 9.75 12.00

by which points am i being misleading?

-

$\frac{n+1}{2}\times 25\% =1.25\\ \frac{n+1}{2}\times 75\% =3.75$
The fivenum command takes the $25^{th}$ percentile as the number half way between $1$ and $7$ and the $75^{th}$ as the number half way between $9$ and $12$, whereas the quantile command may have been an attempt to produce the numbers $0.25$ of the way between $1$ and $7$ and $0.75$ of the way between $9$ and $12$ that contained an error and ended up giving the numbers $0.25$ of the way between 7 and 1 and $0.75$ of the way between $12$ and $9$.