Question

Use the tables to answer the 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 is the same for both tables. The average deviation is the same for both tables. The average deviation cannot be determined from this data set. The average deviation cannot be determined from this data set. The first table has a larger average deviation. The first table has a larger average deviation. The second table has a larger average deviation.

Answer 1

To determine the average deviation for both tables, we will first calculate the average deviation for each dataset based on the provided distances from the mean.

Table 1:

• Distances from mean: 2, 0, 2, 3, 5, 2, 0
• Number of data points: 7

To find the average deviation:

1. Sum the distances: \(2 + 0 + 2 + 3 + 5 + 2 + 0 = 14\)
2. Divide by the number of data points: \( \frac{14}{7} = 2\)

Average Deviation for Table 1 = 2

Table 2:

• Distances from mean: 1, 1, 4, 1, 1, 2, 2
• Number of data points: 7

To find the average deviation:

1. Sum the distances: \(1 + 1 + 4 + 1 + 1 + 2 + 2 = 12\)
2. Divide by the number of data points: \( \frac{12}{7} \approx 1.71\)

Average Deviation for Table 2 ≈ 1.71

Comparison:

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

Now we can conclude:

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

Answer:

The first table has a larger average deviation.