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

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.
Skip to navigation

Answer 1

To determine which graph has a larger standard deviation, we need to analyze the distribution of the data points represented in the first graph, since we do not have specific data from the second graph.

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

**Calculating the Mean for Graph 1:**
Total number of dots = 2 + 4 + 5 + 3 + 2 + 2 = 18
Total sum of values = (0*2) + (1*4) + (2*5) + (3*3) + (4*2) + (5*2) = 0 + 4 + 10 + 9 + 8 + 10 = 41
Mean = Total sum / Total number of dots = 41 / 18 ≈ 2.28

**Calculating the Variance for Graph 1:**
Variance = (Σ (xi - mean)² * frequency) / N
where xi is the value and frequency is the count of that value.

- For 0: (0 - 2.28)² * 2 = 10.4384 * 2 = 20.8768
- For 1: (1 - 2.28)² * 4 = 1.6124 * 4 = 6.4496
- For 2: (2 - 2.28)² * 5 = 0.0784 * 5 = 0.392
- For 3: (3 - 2.28)² * 3 = 0.5184 * 3 = 1.5552
- For 4: (4 - 2.28)² * 2 = 2.9584 * 2 = 5.9168
- For 5: (5 - 2.28)² * 2 = 7.2976 * 2 = 14.5952

Total variance = (20.8768 + 6.4496 + 0.392 + 1.5552 + 5.9168 + 14.5952) / 18 ≈ 2.78
Standard deviation = √variance ≈ √2.78 ≈ 1.67

**For Graph 2:**
We cannot compute the standard deviation without specific data.

**Conclusion:**
Since we can conclude the standard deviation for Graph 1 but cannot determine anything about Graph 2, it is impossible to compare the two based on the provided information.

The correct answer is: **It is impossible to tell from this data.**