Use the images to answer the question.

Question

Graph 1
number line: 0 1 2 3 4 5
Data: 2 4 5 3 2 2

Graph 2
Number line: 4 5 6 7 8 9 10 11 12
data: 0 1 2 3 5 5 3 1 0

Which of the two graphs has a larger standard deviation?

(1 point)
Responses

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

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

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.
The standard deviation is the same for both graphs.
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Answer 1

To determine which graph has a larger standard deviation, we need to calculate the standard deviation for both datasets provided.

Graph 1: Data points: 2, 4, 5, 3, 2, 2.

1. Calculate the mean: Mean = (2 + 4 + 5 + 3 + 2 + 2) / 6 = 18 / 6 = 3.

2. Calculate the squared differences from the mean:

   • (2 - 3)² = 1
   • (4 - 3)² = 1
   • (5 - 3)² = 4
   • (3 - 3)² = 0
   • (2 - 3)² = 1
   • (2 - 3)² = 1

3. Calculate the variance: Variance = (1 + 1 + 4 + 0 + 1 + 1) / 6 = 8 / 6 = 1.33.

4. Calculate the standard deviation: Standard Deviation = √(1.33) ≈ 1.15.

Graph 2: Data points: 0, 1, 2, 3, 5, 5, 3, 1, 0.

1. Calculate the mean: Mean = (0 + 1 + 2 + 3 + 5 + 5 + 3 + 1 + 0) / 9 = 20 / 9 ≈ 2.22.

2. Calculate the squared differences from the mean:

   • (0 - 2.22)² ≈ 4.93
   • (1 - 2.22)² ≈ 1.49
   • (2 - 2.22)² ≈ 0.05
   • (3 - 2.22)² ≈ 0.60
   • (5 - 2.22)² ≈ 7.66
   • (5 - 2.22)² ≈ 7.66
   • (3 - 2.22)² ≈ 0.60
   • (1 - 2.22)² ≈ 1.49
   • (0 - 2.22)² ≈ 4.93

3. Calculate the variance: Variance = (4.93 + 1.49 + 0.05 + 0.60 + 7.66 + 7.66 + 0.60 + 1.49 + 4.93) / 9 ≈ 2.94.

4. Calculate the standard deviation: Standard Deviation = √(2.94) ≈ 1.72.

Comparison:

• Standard deviation for Graph 1 ≈ 1.15
• Standard deviation for Graph 2 ≈ 1.72

Conclusion: The second graph has a larger standard deviation.

Answer: The second graph has a larger standard deviation.