College

Q37.

The mean mass of a squad of 19 hockey players is 82 kg. A player of mass 93 kg joins the squad.

Work out the mean mass of the squad now.

Answer :

To solve the problem of finding the new mean mass of the hockey squad after a player with mass 93 kg joins, we can follow these detailed steps:

1. Calculate the total initial mass of the squad:
- There are initially 19 players.
- The mean mass of the players is 82 kg.
- The total initial mass of the squad is given by:
[tex]\[
\text{Total Initial Mass} = \text{Number of Players} \times \text{Mean Mass}
\][/tex]
Substituting the known values:
[tex]\[
\text{Total Initial Mass} = 19 \times 82 = 1558 \text{ kg}
\][/tex]

2. Calculate the new total mass after the new player joins:
- The mass of the new player joining the squad is 93 kg.
- The new total mass is the sum of the initial total mass and the mass of the new player:
[tex]\[
\text{New Total Mass} = \text{Total Initial Mass} + \text{New Player's Mass}
\][/tex]
Substituting the known values:
[tex]\[
\text{New Total Mass} = 1558 + 93 = 1651 \text{ kg}
\][/tex]

3. Calculate the new number of players in the squad:
- Initially, there were 19 players.
- One new player has joined.
- The new total number of players is:
[tex]\[
\text{New Number of Players} = \text{Initial Number of Players} + 1
\][/tex]
Substituting the known values:
[tex]\[
\text{New Number of Players} = 19 + 1 = 20
\][/tex]

4. Calculate the new mean mass of the squad:
- The new mean mass is calculated by dividing the new total mass by the new number of players:
[tex]\[
\text{New Mean Mass} = \frac{\text{New Total Mass}}{\text{New Number of Players}}
\][/tex]
Substituting the known values:
[tex]\[
\text{New Mean Mass} = \frac{1651}{20}
\][/tex]
Performing the division:
[tex]\[
\text{New Mean Mass} = 82.55 \text{ kg}
\][/tex]

Thus, the new mean mass of the squad after the new player joins is 82.55 kg.

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