Question

The average height of 10 basketball players is 160 cm. If the height of the coach is considered the average increases by 0.5 cm. What is the height of the coach?
A.165.5 cm
B.160.5 cm
C.159.5 cm
D.161.5 cm

Answer 1

Hint: Find the sum of the heights of all the 10 basketball players. Calculate the new average when the height of the coach is added. Now, calculate the sum of heights of 11 persons that is 10 basketball players and 1 coach. The difference in the above sums will give the height of the coach.

Complete step-by-step answer:
We know that the average height of 10 basketball players is 160 cm. We can say that the sum of heights of all 10 players will be, $160 \times 10 = 1600{\text{cm}}$.
When the height of the coach is added, the average height increases by 0.5 cm, that is, the average height becomes, $160 + 0.5 = 160.5{\text{cm}}$.
That is, the average of 11 persons is 160.5cm
Hence, the sum of heights of 10 basketball players and the coach is, $160.5 \times 11 = 1765.5{\text{cm}}$.
Let the height of the coach be $x$.
Then, according to the question, we have $x = 1765.5 - 1600$
Hence, height of the coach is $x = 165.5{\text{cm}}$
Hence, option A is the correct answer.

Note: Average is given by $\dfrac{{{\text{Sum of observations}}}}{{{\text{Number of observations}}}}$. Therefore, the average multiplied by the number of observations gives the total sum of observations. The difference between the sum of 10 basketball players and the sum of 10 basketball players along with the coach is the height of the coach.