Question

1. the number of points jadas basketball team scored in their games have a mean of about 44 and a standard deviation of about 15.7 points. interpret the mean and standard deviation in the context of jadas basketball team.

Explanation:

Step1: Explain the meaning of mean

The mean of \(44\) represents the average number of points Jada's basketball team scored per game. If we consider all the games played, when we distribute the total points scored equally among all the games, each game would account for approximately \(44\) points. Mathematically, if there are \(n\) games and the total points scored is \(T\), then \(\bar{x}=\frac{T}{n} = 44\).

Step2: Explain the meaning of standard deviation

The standard deviation of about \(15.7\) points measures the amount of variation or dispersion in the number of points scored per game. A standard deviation of \(15.7\) means that most of the game - scores are within \(15.7\) points of the mean score of \(44\). In a normal - distribution (a common assumption for such data in a statistical context, although not explicitly stated here), about \(68\%\) of the data (game - scores) lies within the interval \((44 - 15.7,44+15.7)=(28.3,59.7)\), about \(95\%\) lies within \((44-2\times15.7,44 + 2\times15.7)=(12.6,75.4)\) and about \(99.7\%\) lies within \((44-3\times15.7,44+3\times15.7)=(-2.7,90.7)\). Since the number of points scored cannot be negative, in the context of basketball scores, it still gives an idea of how spread out the scores are around the mean of \(44\).

Answer:

The mean of \(44\) is the average number of points per game. The standard deviation of about \(15.7\) measures the spread of points around the mean.