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 $\dfrac{{{x_1} + {x_2} + ......... + {x_n}}}{n}$ and for the median we have the two cases which are
If the total number of terms are even then ${\text{median}} = \dfrac{{\left( {\dfrac{n}{2}} \right){\text{th term}} + \left( {\dfrac{n}{2} + 1} \right){\text{th term}}}}{2}$
For $n = $odd we get that ${\text{median}} = \left( {\dfrac{{n + 1}}{2}} \right){\text{th term}}$

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$ = $ $\dfrac{{{x_1} + {x_2} + ......... + {x_n}}}{n}$
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$ = \dfrac{{{x_1} + {x_2} + ......... + {x_7}}}{7} = \dfrac{{180 + 178 + 176 + 181 + 190 + 175 + 187}}{7} = \dfrac{{1267}}{7} = 181$
For team B we will get that
Mean$ = \dfrac{{{x_1} + {x_2} + ......... + {x_7}}}{7} = \dfrac{{174 + 175 + 190 + 179 + 178 + 185 + 177}}{7} = \dfrac{{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
${\text{median}} = \left( {\dfrac{{n + 1}}{2}} \right){\text{th term}}$
For team A
${\text{median}} = \left( {\dfrac{{7 + 1}}{2}} \right){\text{th term}} = 4th{\text{ term}} = 180$
For team B
${\text{median}} = \left( {\dfrac{{7 + 1}}{2}} \right){\text{th term}} = 4th{\text{ term}} = 178$

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