Question
Bryan calculates the mean and average deviation from the mean for two datasets: Set A, which includes the numbers {30,33,42,42,42,51,54}
, and Set B, which includes the numbers {21,29,34,42,50,55,63}
. Which statement is true?(1 point)
Responses
The average deviation from the mean for Set A is 12, but the average deviation from the mean for Set B is 6.
The average deviation from the mean for Set A is 12, but the average deviation from the mean for Set B is 6.
For each set, the average deviation from the mean is 0.
For each set, the average deviation from the mean is 0.
For each set, the average deviation from the mean is 42.
For each set, the average deviation from the mean is 42.
The average deviation from the mean for Set A is 6, but the average deviation from the mean for Set B is 12.
, and Set B, which includes the numbers {21,29,34,42,50,55,63}
. Which statement is true?(1 point)
Responses
The average deviation from the mean for Set A is 12, but the average deviation from the mean for Set B is 6.
The average deviation from the mean for Set A is 12, but the average deviation from the mean for Set B is 6.
For each set, the average deviation from the mean is 0.
For each set, the average deviation from the mean is 0.
For each set, the average deviation from the mean is 42.
For each set, the average deviation from the mean is 42.
The average deviation from the mean for Set A is 6, but the average deviation from the mean for Set B is 12.
Answers
GPT-4o mini
To determine the average deviation from the mean for both datasets Set A and Set B, we first need to calculate the mean and then the average deviation from the mean.
### Set A: {30, 33, 42, 42, 42, 51, 54}
1. **Calculate the Mean**:
\[
\text{Mean} = \frac{30 + 33 + 42 + 42 + 42 + 51 + 54}{7} = \frac{294}{7} = 42
\]
2. **Calculate the Average Deviation**:
- Deviations from the mean:
- |30 - 42| = 12
- |33 - 42| = 9
- |42 - 42| = 0
- |42 - 42| = 0
- |42 - 42| = 0
- |51 - 42| = 9
- |54 - 42| = 12
- Sum of deviations = 12 + 9 + 0 + 0 + 0 + 9 + 12 = 42
- Average Deviation:
\[
\text{Average Deviation} = \frac{42}{7} = 6
\]
### Set B: {21, 29, 34, 42, 50, 55, 63}
1. **Calculate the Mean**:
\[
\text{Mean} = \frac{21 + 29 + 34 + 42 + 50 + 55 + 63}{7} = \frac{294}{7} = 42
\]
2. **Calculate the Average Deviation**:
- Deviations from the mean:
- |21 - 42| = 21
- |29 - 42| = 13
- |34 - 42| = 8
- |42 - 42| = 0
- |50 - 42| = 8
- |55 - 42| = 13
- |63 - 42| = 21
- Sum of deviations = 21 + 13 + 8 + 0 + 8 + 13 + 21 = 84
- Average Deviation:
\[
\text{Average Deviation} = \frac{84}{7} = 12
\]
### Conclusion:
- The average deviation from the mean for Set A is **6**.
- The average deviation from the mean for Set B is **12**.
Thus, the correct statement is:
**The average deviation from the mean for Set A is 6, but the average deviation from the mean for Set B is 12.**
### Set A: {30, 33, 42, 42, 42, 51, 54}
1. **Calculate the Mean**:
\[
\text{Mean} = \frac{30 + 33 + 42 + 42 + 42 + 51 + 54}{7} = \frac{294}{7} = 42
\]
2. **Calculate the Average Deviation**:
- Deviations from the mean:
- |30 - 42| = 12
- |33 - 42| = 9
- |42 - 42| = 0
- |42 - 42| = 0
- |42 - 42| = 0
- |51 - 42| = 9
- |54 - 42| = 12
- Sum of deviations = 12 + 9 + 0 + 0 + 0 + 9 + 12 = 42
- Average Deviation:
\[
\text{Average Deviation} = \frac{42}{7} = 6
\]
### Set B: {21, 29, 34, 42, 50, 55, 63}
1. **Calculate the Mean**:
\[
\text{Mean} = \frac{21 + 29 + 34 + 42 + 50 + 55 + 63}{7} = \frac{294}{7} = 42
\]
2. **Calculate the Average Deviation**:
- Deviations from the mean:
- |21 - 42| = 21
- |29 - 42| = 13
- |34 - 42| = 8
- |42 - 42| = 0
- |50 - 42| = 8
- |55 - 42| = 13
- |63 - 42| = 21
- Sum of deviations = 21 + 13 + 8 + 0 + 8 + 13 + 21 = 84
- Average Deviation:
\[
\text{Average Deviation} = \frac{84}{7} = 12
\]
### Conclusion:
- The average deviation from the mean for Set A is **6**.
- The average deviation from the mean for Set B is **12**.
Thus, the correct statement is:
**The average deviation from the mean for Set A is 6, but the average deviation from the mean for Set B is 12.**