Question

Use the images to answer the question.

Graph 1

An unlabeled dot plot. The dot plot has arrows at both ends and ranges from 0 to 5 in increments of 1. There are 2 dots above 0, 4 dots above 1, 5 dots above 2, 3 dots above 3, 2 dots above 4, and 2 dots above 5.

Graph 2

An unlabeled dot plot.

Which of the two graphs has a larger standard deviation?

(1 point)
Responses

It is impossible to tell from this data.
It is impossible to tell from this data.

The first graph has a larger standard deviation.
The first graph has a larger standard deviation.

The second graph has a larger standard deviation.
The second graph has a larger standard deviation.

The standard deviation is the same for both graphs.

Answer 1

To determine which graph has a larger standard deviation, we need to analyze the spread of data in both dot plots, even though we only have detailed information about the first graph.

**Graph 1 Data:**
- 0: 2 dots
- 1: 4 dots
- 2: 5 dots
- 3: 3 dots
- 4: 2 dots
- 5: 2 dots

To find a rough estimate of the variance and standard deviation, we can calculate the mean of the data points. The total number of occurrences (dots) is:

\[
Total = 2 + 4 + 5 + 3 + 2 + 2 = 18
\]

Now calculate the mean (average):

\[
Mean = \frac{(0 \cdot 2 + 1 \cdot 4 + 2 \cdot 5 + 3 \cdot 3 + 4 \cdot 2 + 5 \cdot 2)}{Total}
\]

\[
Mean = \frac{(0 + 4 + 10 + 9 + 8 + 10)}{18} = \frac{41}{18} \approx 2.28
\]

Next, to find the variance, we would typically find the squared differences from the mean, multiply by frequency, and then average. However, without the second graph, we cannot perform a comparison here.

Since we do not have the second graph's data (Graph 2), we cannot calculate its mean and standard deviation. Therefore, we cannot ascertain which graph has a larger standard deviation based on the provided data.

The conclusion is:

**It is impossible to tell from this data.**