Answer :
Let's go through step-by-step to find Dora's error.
1. Calculate the Mean:
To find the mean, add all the numbers together and divide by the count of numbers.
Numbers: 30, 10, 20, 427, 19
[tex]\[
\text{Mean} = \frac{30 + 10 + 20 + 427 + 19}{5} = 101.2
\][/tex]
2. Find Absolute Deviations:
The absolute deviation for each number is the absolute difference between the number and the mean.
- For 30: [tex]\(|30 - 101.2| = 71.2\)[/tex]
- For 10: [tex]\(|10 - 101.2| = 91.2\)[/tex]
- For 20: [tex]\(|20 - 101.2| = 81.2\)[/tex]
- For 427: [tex]\(|427 - 101.2| = 325.8\)[/tex]
- For 19: [tex]\(|19 - 101.2| = 82.2\)[/tex]
3. Calculate the Mean Absolute Deviation (MAD):
Add up all the absolute deviations and divide by the number of values to find the Mean Absolute Deviation.
[tex]\[
MAD = \frac{71.2 + 91.2 + 81.2 + 325.8 + 82.2}{5} = 130.32
\][/tex]
4. Identify Dora's Error:
Dora’s calculation error, which is dividing by the wrong number, resulted in using only four numbers instead of five when finding the mean absolute deviation.
Dora should have divided by 5, not 4, when calculating the Mean Absolute Deviation.
Therefore, the error in the solution is: "Dora used only four numbers in finding the mean absolute deviation."
1. Calculate the Mean:
To find the mean, add all the numbers together and divide by the count of numbers.
Numbers: 30, 10, 20, 427, 19
[tex]\[
\text{Mean} = \frac{30 + 10 + 20 + 427 + 19}{5} = 101.2
\][/tex]
2. Find Absolute Deviations:
The absolute deviation for each number is the absolute difference between the number and the mean.
- For 30: [tex]\(|30 - 101.2| = 71.2\)[/tex]
- For 10: [tex]\(|10 - 101.2| = 91.2\)[/tex]
- For 20: [tex]\(|20 - 101.2| = 81.2\)[/tex]
- For 427: [tex]\(|427 - 101.2| = 325.8\)[/tex]
- For 19: [tex]\(|19 - 101.2| = 82.2\)[/tex]
3. Calculate the Mean Absolute Deviation (MAD):
Add up all the absolute deviations and divide by the number of values to find the Mean Absolute Deviation.
[tex]\[
MAD = \frac{71.2 + 91.2 + 81.2 + 325.8 + 82.2}{5} = 130.32
\][/tex]
4. Identify Dora's Error:
Dora’s calculation error, which is dividing by the wrong number, resulted in using only four numbers instead of five when finding the mean absolute deviation.
Dora should have divided by 5, not 4, when calculating the Mean Absolute Deviation.
Therefore, the error in the solution is: "Dora used only four numbers in finding the mean absolute deviation."
