Ask a New Question
Menu

Use the tables to answer the 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 first table has a larger average deviation.
The first table has a larger average deviation.

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.

1 answer

To determine the average deviation for both datasets, we need to calculate the average of the "Distance from Mean" values for each table.

For Table 1:

  • Distance from Mean values: 0, 4, 2, 1, 0, 1, 1, 1, 2
  • Sum of distances = 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 (approximately)

For Table 2:

  • Distance from Mean values: 2, 1, 3, 3, 1, 1, 1, 1, 2
  • Sum of distances = 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 (approximately)

Now comparing the average deviations:

  • Table 1 Average Deviation: 1.33
  • Table 2 Average Deviation: 1.67

Since 1.67 (from Table 2) is greater than 1.33 (from Table 1), the correct response is:

The second table has a larger average deviation.