Question

1. the box plot represents the distribution of the number of points scored by a cross country team at 12 meets. (lesson 1 - 2)

a. if possible, find the mean. if not possible, explain why not.
b. if possible, find the median. if not possible, explain why not.
c. did the cross country team ever score 30 points at a meet?

Explanation:

Step1: Analyze the mean calculation

To find the mean, we need the sum of all data values and the number of data values. A box - plot does not provide the individual data points. So, we cannot calculate the sum of the data values.

Step2: Analyze the median calculation

The median is the middle value of a data set. In a box - plot, the line inside the box represents the median.

Step3: Analyze the data point 30

A box - plot shows the range (minimum, first quartile, median, third quartile, maximum) of the data. It does not show if a particular value (in this case 30) was actually achieved. The box - plot only gives information about the spread and central tendency in terms of quartiles and median, not individual data points.

Answer:

a. Not possible. A box - plot does not give individual data points needed to calculate the sum for the mean formula \( \bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\).
b. The median is the line inside the box. From the box - plot, the median is 32.
c. We cannot be sure. A box - plot does not show individual data points; it only shows the minimum, \(Q_1\), median, \(Q_3\), and maximum values of the data set.