Question

4/ The table shows the heights of players in a basketball team. Height (cm) Frequency a) Work out the mean height of the team. Round your answer to 1 decimal place. 198 199 200 2 b) A new player joins the team and raises the mean average height to 201 cm. 201 202 2 Work out the height of this new player.

Answer 1

Answer:

Step-by-step explanation:

Hello!

The table shows the heights in a basketball team.

Height:       198, 199, 200, 201, 202

Frequency:   1,      3,     2,     5,     2

a.) Work out the mean height of the team. Round your answer to 1d.p.

Since the heights of the basketball players is arranged in a frequency table, to calculate the mean you have to use the following formula:

X[bar]= (∑Xfi)/n= (198*1+199*3+200*2+201*5+202*2)/13= 2604/13= 200.307= 200.3 cm

b.) A new player joins the team and raises the mean average height to 201 cm. Work out the height of the new player.

X[bar]ₙ₊₁= 201 cm

This mean was obtained using the same formula as in item a) but with an n'= 14 instead of 13, assuming non of the other players has left the team, so for them ∑Xfi= 2604 cm and "b" will represent the height of the new player:

X[bar]ₙ₊₁=  ((∑Xfi)+b)/(n+1)= (2604+b)/14= 201 cm

2604+b= 201*14

2604+b=2814

b= 2814-2604= 210 cm

The new player's height is 210 cm

I hope this helps!