Question

from unit 1, lesson 2
the box plot represents the distribution of the number of points scored by a cross country team at 12 meets.
a. if possible, find the mean. if not possible, explain why not.
box plot with number line labeled points from 22 to 42, ticks at 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, and a box between 32 and 38, whiskers extending to 22 and 42

Explanation:

Step1: Understand Box Plot Limitation

A box plot shows the five - number summary (minimum, first quartile, median, third quartile, maximum) and the distribution shape (like spread, skewness), but it does not provide the individual data points or the frequency of each data point. The mean is calculated as $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the individual data values and $n$ is the number of data points. Since we don't know the exact values of each of the 12 data points (we only know the summary statistics from the box plot), we can't compute the sum of the data points.

Step2: Conclusion on Mean Calculation

To find the mean, we need the actual values of all the data points to calculate their sum and then divide by the number of data points (12 in this case). The box plot does not give us the individual values, so we don't have enough information to compute the sum of the points scored.

Answer:

It is not possible to find the mean from the box plot alone. A box plot only provides the five - number summary (minimum, $Q_1$, median, $Q_3$, maximum) and information about the distribution's spread and shape, but it does not give the individual data points or their frequencies, which are needed to calculate the mean (since the mean requires summing all data points and dividing by the number of data points).