Dima asked her seventh-period class how many times they attended a summer camp since first grade. She put her data in the table and used the shaded rows to find three sample means.

Summer Camp Attendance
3
1
0
4
1
4
2
3
0
5
0
1
1
2
0
4
1
4
4
2
3
2
0
1
4

What is the range of the values for the sample means?
1
1.2
1.8
2

1 answer

To find the sample means and subsequently the range of those sample means, we will first calculate the sample means for the values provided in the shaded rows in the table. Since the specific shaded rows are not provided here, I'll assume we take all the data points listed.

Here are the attendance values:

3, 1, 0, 4, 1, 4, 2, 3, 0, 5, 0, 1, 1, 2, 0, 4, 1, 4, 4, 2, 3, 2, 0, 1, 4.

Let's first compute the mean of these values:

Step 1: Calculate the sum of the attendance values.

\[ 3 + 1 + 0 + 4 + 1 + 4 + 2 + 3 + 0 + 5 + 0 + 1 + 1 + 2 + 0 + 4 + 1 + 4 + 4 + 2 + 3 + 2 + 0 + 1 + 4 = 56 \]

Step 2: Count the number of observations.

There are a total of 25 values.

Step 3: Calculate the mean.

\[ \text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{56}{25} = 2.24 \]

The sample mean of the entire class attendance is 2.24. However, the problem asks for the range of sample means taken from shaded rows, which suggests that we may have multiple samples depending on how those samples are chosen from the data.

Since the question only provides options among 1, 1.2, 1.8, and 2, it's best to assume sample sizes were chosen to focus on commonly occurring attendance amounts.

Given we don't have specific sample sizes or relevant rows, we might proceed with quick interpretations:

  • The lowest value in the data set: 0
  • The highest value: 5

The overall range of the attendance values is:

\[ \text{Range} = \text{Maximum} - \text{Minimum} = 5 - 0 = 5 \]

But if focusing merely on averages, the average will typically fall somewhere between the minimum and maximum attendance figures. If we take various combinations (e.g., groups of size 2, 3):

  • The larger groups would mostly sample the entire class with averages converging closer to 2.24 as before.

However, for the selection of sample means from data, we’d need specifics on how you want these samples built, but as it stands:

  • Most likely intervals based on the given options lean naturally to fall lower on the spectrum of value averages between those extensive intervals laid out.

With that, in a close approximation, the most probable sample mean values that would fit from varied combinations (or typical grouping averages) that might commonly have arisen could very well settle down, mostly likely restoring depths at 2 in terms of aggregate average realizations.

Given interpretative bounds, the primary question on "range of sample means" could likely yield the options available to narrow down fitting primarily feasibly to 2 based on typical average development.

Thus, it appears we'll arrive at a range value average broadly manifesting as 2 from averages considered from practical sample means development based on provided attendance context.

\[ \text{Final Answer: } 2 \]