in 4 games, larry averaged 23 ppg (points per game). how many points does he need to score in the last game…
in 4 games, larry averaged 23 ppg (points per game). how many points does he need to score in the last game to have an average of 25 ppg? explain how to use the mean and the data given to find the answer.
Answer
Explanation:
Step1: Find total points in 4 games
The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Given $n = 4$ and $\bar{x}=23$, the total points in 4 games $\sum_{i = 1}^{4}x_{i}=n\times\bar{x}=4\times23 = 92$.
Step2: Find total points needed in 5 games
If the average for 5 games is to be 25 PPG, and $n = 5$, then the total points needed $\sum_{i = 1}^{5}x_{i}=n\times\bar{x}=5\times25=125$.
Step3: Find points for the 5th game
Let the points in the 5th game be $x_5$. We know that $\sum_{i = 1}^{5}x_{i}=\sum_{i = 1}^{4}x_{i}+x_5$. So $x_5=\sum_{i = 1}^{5}x_{i}-\sum_{i = 1}^{4}x_{i}=125 - 92=33$.
Answer:
33