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

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

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

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

The first table has a larger average deviation.

Answer 1

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

Table 1

Distance from Mean: 0, 4, 2, 1, 0, 1, 1, 1, 2
Total Distance: 0 + 4 + 2 + 1 + 0 + 1 + 1 + 1 + 2 = 12
Number of Data Points: 9
Average Deviation: \( \frac{12}{9} = \frac{4}{3} \approx 1.33 \)

Table 2

Distance from Mean: 2, 1, 3, 3, 1, 1, 1, 1, 2
Total Distance: 2 + 1 + 3 + 3 + 1 + 1 + 1 + 1 + 2 = 15
Number of Data Points: 9
Average Deviation: \( \frac{15}{9} = \frac{5}{3} \approx 1.67 \)

Comparison

• Average Deviation of Table 1: \( \approx 1.33 \)
• Average Deviation of Table 2: \( \approx 1.67 \)

Conclusion

The second table has a larger average deviation than the first table.

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