Question

what percentage of traes games had 22 points or more?

Explanation:

Step1: Determine the total number of games

In a box - and - whisker plot, the total number of data points (games in this case) can be thought of in terms of the quartiles. The entire data set is divided into four quartiles. The formula for the number of data points \(n\) (assuming a non - fractional number of data points based on quartile positions) can be considered as follows: The minimum value is \(12\), the first quartile \(Q_1 = 22\), the median \(Q_2=30\), the third quartile \(Q_3 = 35.5\), and the maximum value is \(47\).
We can use the fact that the number of data points \(n\) (if we assume a simple non - fractional count based on the spread and quartile definitions) can be calculated using the formula for the position of quartiles. For a set of data ordered from smallest to largest, if \(n\) is the number of data points, the first quartile \(Q_1\) is at position \(\frac{n + 1}{4}\), the median \(Q_2\) is at position \(\frac{n+1}{2}\), and the third quartile \(Q_3\) is at position \(\frac{3(n + 1)}{4}\).
Let's assume \(n\) is such that the spread from the minimum to the maximum and the quartile positions make sense. We can also use a simple count - like approach. The number of data points is \(n=4\) (quartiles) times some integer plus the minimum and maximum. A more straightforward way (since we know the values of quartiles and min/max) is to consider that the number of data points \(n\) can be thought of as \(n = 4k\) (for some positive integer \(k\)) plus the min and max. If we assume a simple case, we can use the formula for the percentage: \(\text{Percentage}=\frac{\text{Number of games with }x\geq22}{\text{Total number of games}}\times100\)
The number of games with \(x\geq22\) is \(n_1\). The minimum value is \(12\). The first quartile \(Q_1 = 22\). The number of data points in the upper three - quartiles (since \(Q_1\) is the value below which \(25\%\) of the data lies) is \(n_1=\frac{3}{4}n\).
If we assume \(n = 4\) (for simplicity, since quartiles divide the data into four parts), the number of data points with \(x\geq22\) (the value of \(Q_1\)) is \(3\). But a better way is to use the formula for the percentage. The proportion of data points with \(x\geq Q_1\) is \(75\%\) (because \(Q_1\) is the \(25^{th}\) percentile).
Mathematically, if \(P\) is the percentage, and \(p\) is the proportion. We know that if \(x\) is a data point and \(x\geq Q_1\), the proportion \(p = 1-0.25\) (since \(Q_1\) is the \(25^{th}\) percentile).

Step2: Calculate the percentage

Using the formula \(P=p\times100\), where \(p = 0.75\) (because the proportion of data points greater than or equal to the first quartile \(Q_1\) is \(1 - 0.25\)).
\(P=0.75\times100\)

Answer:

\(75\%\)