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 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. It is impossible to tell from this data. It is impossible to tell from this data. The first table has a larger average deviatio

Answer 1

To determine the average deviation for both tables, we first need to find the average distance from the mean for each dataset.

Table 1:

• Distance from Mean: 0, 4, 2, 1, 0, 1, 1, 1, 2

• Average Deviation Calculation: \[ \text{Average Deviation} = \frac{\sum \text{Distance from Mean}}{n} \] where \( n \) is the number of data points.

  \[ \sum \text{Distance from Mean} = 0 + 4 + 2 + 1 + 0 + 1 + 1 + 1 + 2 = 12 \] \[ n = 9 \] \[ \text{Average Deviation} = \frac{12}{9} \approx 1.33 \]

Table 2:

• Distance from Mean: 2, 1, 3, 3, 1, 1, 1, 1, 2
• Average Deviation Calculation: \[ \sum \text{Distance from Mean} = 2 + 1 + 3 + 3 + 1 + 1 + 1 + 1 + 2 = 15 \] \[ n = 9 \] \[ \text{Average Deviation} = \frac{15}{9} \approx 1.67 \]

Conclusion:

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

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