7, 9, 10, 11, 11. what is the average deviation from the mean number

Answer 1

To calculate the average deviation from the mean for the numbers 7, 9, 10, 11, and 11, we first need to find the mean (average) of these numbers.

Step 1: Calculate the Mean

1. Sum the numbers: \( 7 + 9 + 10 + 11 + 11 = 58 \)

2. Count the numbers: There are 5 numbers.

3. Calculate the mean: \( \text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{58}{5} = 11.6 \)

Step 2: Calculate the Deviations from the Mean

Now we will find the absolute deviations from the mean for each number:

• For 7: \( |7 - 11.6| = 4.6 \)
• For 9: \( |9 - 11.6| = 2.6 \)
• For 10: \( |10 - 11.6| = 1.6 \)
• For 11: \( |11 - 11.6| = 0.6 \)
• For 11: \( |11 - 11.6| = 0.6 \)

Step 3: Calculate the Average Deviation

1. Sum the absolute deviations: \( 4.6 + 2.6 + 1.6 + 0.6 + 0.6 = 10.6 \)

2. Calculate the average deviation: \( \text{Average Deviation} = \frac{\text{Sum of Absolute Deviations}}{\text{Count}} = \frac{10.6}{5} = 2.12 \)

Conclusion

The average deviation from the mean is 2.12.