Question

22 24 26 28 30 32 34 36 38 40 42
points

1. if possible, find the mean. if not possible, explain why not.

answer \possible or not possible\:
answer with the letter below for the correct mean number or explanation of why not:
a. 34
b. 42
c. it is not possible to calculate the mean because the total number of meets is not given.
d. it is not possible to calculate the mean because the box - plot does not provide the 12 scores.

1. if possible, find the median. if not possible, explain why not.

answer \possible or not possible\:
answer with the letter below for the correct median number or explanation of why not:
a. 33
b. 34
c. it is not possible to find the median because the box plot does not have all of the data values.
d. it is not possible to find the median because the box plot does not provide the 12 scores.

1. did the cross - country team ever score 30 points at a meet?

answer with the letter for the correct answer:
a. yes, they scored 30 points.
b. no, they did not score 30 points.
c. it is not possible to tell if they scored 30 points

Explanation:

Step1: Recall mean - calculation requirements

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are data - points and $n$ is the number of data - points. A box - plot only shows the five - number summary (minimum, first quartile, median, third quartile, maximum) and not all individual data values. Without all individual data values, we cannot calculate $\sum_{i = 1}^{n}x_{i}$ and we also don't know $n$. So it is not possible to calculate the mean.

Step2: Recall median - calculation for box - plot

The median is represented in a box - plot. For a box - plot, the line inside the box represents the median. Since the box - plot is evenly spaced around 33 (assuming a symmetric distribution based on the given scale), the median is 33.

Step3: Analyze data presence in box - plot

A box - plot does not show every single data value. Just because 30 is on the number line does not mean the team scored 30 points. We cannot tell from the box - plot if the team ever scored 30 points.

Answer:

1. Not Possible; D
2. Possible; A
3. C