Use the tables to answer the question.

Question

Table 1

Data Point 11 15 9 10 11 12 12 10 9
Distance from Mean 0 4 2 1 0 1 1 1 2
Table 2

Data Point 9 10 14 14 12 10 10 10 9
Distance from Mean 2 1 3 3 1 1 1 1 2
Compare the datasets in the tables. Which of the following correctly describes the relationship of their average deviations?

(1 point)
Responses

The first table has a larger average deviation.
The first table has a larger average deviation.

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

The second table has a larger average deviation.
The second table has a larger average deviation.

The average deviation is the same for both tables.
The average deviation is the same for both tables.
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Answer 1

To compare the average deviations of the two datasets, we need to compute the average deviation for each table.

Table 1:

• Distance from Mean: 0, 4, 2, 1, 0, 1, 1, 1, 2
• Sum of distances from the mean = 0 + 4 + 2 + 1 + 0 + 1 + 1 + 1 + 2 = 12
• Number of data points = 9
• Average deviation = Sum of distances / Number of data points = 12 / 9 ≈ 1.33

Table 2:

• Distance from Mean: 2, 1, 3, 3, 1, 1, 1, 1, 2
• Sum of distances from the mean = 2 + 1 + 3 + 3 + 1 + 1 + 1 + 1 + 2 = 15
• Number of data points = 9
• Average deviation = Sum of distances / Number of data points = 15 / 9 ≈ 1.67

Now we can compare the average deviations:

• Table 1 average deviation ≈ 1.33
• Table 2 average deviation ≈ 1.67

Conclusion: The average deviation of the second table is larger.

Thus, the correct response is: The second table has a larger average deviation.