Step 1

We have given that

If a data set has an even number of observations

Step 2

If data set has an even number of observations then Median is

Median \(\displaystyle={\left({\frac{{{\frac{{{n}}}{{{2}}}}-{t}{h}\ {t}{e}{r}{m}+{\left({\frac{{{n}}}{{{2}}}}+{1}\right)}-{t}{h}\ {t}{e}{r}{m}}}{{{2}}}}\right)}\)

For example the data are 1,3,4,5,6,4

The data arrange in increasing order and the increasing order are 1,3,4,4,5,6

\(\displaystyle{M}{e}{d}{i}{a}{n}={\left({\frac{{{\frac{{{6}}}{{{2}}}}-{t}{h}\ {t}{e}{r}{m}+{\left({\frac{{{6}}}{{{2}}}}+{1}\right)}-{t}{h}\ {t}{e}{r}{m}}}{{{2}}}}\right)}\)

\(\displaystyle{M}{e}{d}{i}{a}{n}={\frac{{{3}-{t}{h}\ {t}{e}{r}{m}+{4}-{t}{h}\ {t}{e}{r}{m}}}{{{2}}}}={\frac{{{4}+{4}}}{{{2}}}}={4}\)

We have given that

If a data set has an even number of observations

Step 2

If data set has an even number of observations then Median is

Median \(\displaystyle={\left({\frac{{{\frac{{{n}}}{{{2}}}}-{t}{h}\ {t}{e}{r}{m}+{\left({\frac{{{n}}}{{{2}}}}+{1}\right)}-{t}{h}\ {t}{e}{r}{m}}}{{{2}}}}\right)}\)

For example the data are 1,3,4,5,6,4

The data arrange in increasing order and the increasing order are 1,3,4,4,5,6

\(\displaystyle{M}{e}{d}{i}{a}{n}={\left({\frac{{{\frac{{{6}}}{{{2}}}}-{t}{h}\ {t}{e}{r}{m}+{\left({\frac{{{6}}}{{{2}}}}+{1}\right)}-{t}{h}\ {t}{e}{r}{m}}}{{{2}}}}\right)}\)

\(\displaystyle{M}{e}{d}{i}{a}{n}={\frac{{{3}-{t}{h}\ {t}{e}{r}{m}+{4}-{t}{h}\ {t}{e}{r}{m}}}{{{2}}}}={\frac{{{4}+{4}}}{{{2}}}}={4}\)