Use the images to answer the question.

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

4 to 12 in increments of 1. There are 0 dots above 4, 1 dots above 5, 2 dots above 6, 3 dots above 7, 5 dots above 8, and 5 dots above 9. 3 dots above 10, 1 dot above 11, 0 dots above 12

Which of the two graphs has a larger standard deviation?

(1 point)
Responses

The standard deviation is the same for both graphs.
The standard deviation is the same for both graphs.

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.
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Answer 1

To determine which graph has a larger standard deviation, we need to analyze the spread of the data points in each graph.

Graph 1:

• Data:
  • 0: 2 dots
  • 1: 4 dots
  • 2: 5 dots
  • 3: 3 dots
  • 4: 2 dots
  • 5: 2 dots
• Distribution is centered around 2, with most data points clustered near this value and fewer at the extremes (0 and 5).

Graph 2:

• Data:
  • 4: 0 dots
  • 5: 1 dot
  • 6: 2 dots
  • 7: 3 dots
  • 8: 5 dots
  • 9: 5 dots
  • 10: 3 dots
  • 11: 1 dot
  • 12: 0 dots
• This graph shows a wider spread of data values, with data points ranging from 5 to 11, with a peak around 8 and 9.

Conclusion: The standard deviation is a measure of the spread of a set of values. Graph 2 has a wider range (5 to 11) compared to Graph 1 (0 to 5), indicating that Graph 2 likely has a larger standard deviation due to the greater variance in values.

Therefore, the correct response is:

The second graph has a larger standard deviation.