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

The mean height of the team is 200 cm.

The height of the new player is 206 cm.

To calculate the mean height of the team, you can use the formula:

Mean= Sum of all heights / Number of players

Let's calculate it:

Mean= (198+199+200+201+202)/5

Mean= 1000/5

Mean=200

So, the mean height of the team is 200 cm.

Now, for part b), let's denote the height of the new player as

x. The new mean height is given as 201 cm. The new mean can be calculated using the formula:

New Mean= Sum of all heights including the new player/ Number of players + 1

201= (198+199+200+201+202+x)/6

​Now, solve for x:

201×6=1000+x

1206=1000+x

x=206

So, the height of the new player is 206 cm.

Answer 2

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!