Question

1. use structure the school basketball team had the following scores for its games this year: 47, 36, 42, 29, 39, 49, 44, and 32. estimate how many points they scored this year. explain your estimate.

Explanation:

Step1: Find the average of the scores from this year

First, sum up the scores from this year: \(47+36 + 42+29+39=193\). Then divide by the number of games (\(n = 5\)) to get the average. The average \(\bar{x}=\frac{193}{5}=38.6\)

Step2: Estimate the total points for next - year

Assume the number of games next year is also \(n = 5\). Multiply the average score (\(\bar{x}=38.6\)) by the number of games. The estimated total points \(T=38.6\times5 = 193\) (we can also use a simpler approach: round \(38.6\) to \(40\), then \(40\times5=200\))

Answer:

An estimate of the points they scored this year (assuming 5 games next year) is about \(200\) (if we round the average of this - year's scores to a whole number for estimation). If we use the non - rounded average \(\frac{47 + 36+42+29+39}{5}=\frac{193}{5}=38.6\), then \(38.6\times5 = 193\). But for an estimate, rounding the average (e.g., \(38.6\approx40\)) gives a more intuitive estimate. So a reasonable estimate is \(200\) points.