Use the tables to answer the question.

Question

Table 1

Data Point 13 15 13 12 20 17 15
Distance from Mean 2 0 2 3 5 2 0
Table 2

Data Point 14 16 19 16 14 13 13
Distance from Mean 1 1 4 1 1 2 2


Compare the datasets in the tables. Which of the following correctly describes the relationship of their average deviations?

(1 point)
Responses

The average deviation cannot be determined from this data set.
The average deviation cannot be determined from this data set.

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 determine the average deviation for each dataset in the tables, we can follow these steps:

1. Calculate the sum of the distances from the mean for each table.
2. Divide by the number of data points.

Table 1:

• Distances from the mean: 2, 0, 2, 3, 5, 2, 0
• Sum of distances: \(2 + 0 + 2 + 3 + 5 + 2 + 0 = 14\)
• Number of data points: 7
• Average deviation for Table 1: \(\frac{14}{7} = 2\)

Table 2:

• Distances from the mean: 1, 1, 4, 1, 1, 2, 2
• Sum of distances: \(1 + 1 + 4 + 1 + 1 + 2 + 2 = 12\)
• Number of data points: 7
• Average deviation for Table 2: \(\frac{12}{7} \approx 1.71\)

Now, we compare the average deviations:

• Average deviation for Table 1 = 2
• Average deviation for Table 2 ≈ 1.71

Since 2 (Table 1) is greater than 1.71 (Table 2), we conclude that the first table has a larger average deviation.

Therefore, the correct response is:

The first table has a larger average deviation.