Question

The height (in cm) of the volleyball players from team A and team B were recorded as
Team A: $180,178,176,181,190,175,187$
Team B: $174,175,190,179,178,185,177$
Which team has the greatest average height?
Find the median of team A and team B.

Answer 1

Hint: Average height is another name for the mean height and we know that mean of the numbers $x_1,x_2,x_3,...........x_n$ is given by ${\displaystyle \frac{x_1+x_2+.........+x_n}{n}}$ and for the median we have the two cases which are
If the total number of terms are even then $\text{median}={\displaystyle \frac{\left({\displaystyle \frac{n}{2}}\right)\text{th term}+\left({\displaystyle \frac{n}{2}}+1\right)\text{th term}}{2}}$
For $n=$odd we get that $\text{median}=\left({\displaystyle \frac{n+1}{2}}\right)\text{th term}$

Complete step-by-step answer:
Here in the question we are given the heights of the team A and the team B in cm as
Team A: $180,178,176,181,190,175,187$
Team B: $174,175,190,179,178,185,177$
We need to find the average height of both and find which team has the higher average height. So if we take the team A we have $7$ players whose heights are given as $180,178,176,181,190,175,187$\
For the numbers $x_1,x_2,x_3,...........x_n$mean is given by
Mean$=$ ${\displaystyle \frac{x_1+x_2+.........+x_n}{n}}$
For these $7$ players we find the man in the same way for team A and the team B
For team A we get that
Mean$={\displaystyle \frac{x_1+x_2+.........+x_7}{7}}={\displaystyle \frac{180+178+176+181+190+175+187}{7}}={\displaystyle \frac{1267}{7}}=181$
For team B we will get that
Mean$={\displaystyle \frac{x_1+x_2+.........+x_7}{7}}={\displaystyle \frac{174+175+190+179+178+185+177}{7}}={\displaystyle \frac{1258}{7}}=179.71$
So its average height is $179.71cm$
As we know for the median we can apply the above formula but only when we have the terms arranged in the ascending or descending order as follows
Team A$=175,176,178,180,181,187,190$
Team B$=178,175,177,178,179,185,190$
As the terms are odd which is seven so we apply the formula as
$\text{median}=\left({\displaystyle \frac{n+1}{2}}\right)\text{th term}$
For team A
$\text{median}=\left({\displaystyle \frac{7+1}{2}}\right)\text{th term}=4th\text{ term}=180$
For team B
$\text{median}=\left({\displaystyle \frac{7+1}{2}}\right)\text{th term}=4th\text{ term}=178$

Note: If we are given the value of mean and median then we can find the mode by using the given formula
$\text{mode}=3\text{median}-2\text{mean}$