Question
Tammy’s last four homework scores were 68, 76, 70, and 74. The mean absolute deviation of her scores is
.
Tammy worked hard on yesterday’s assignment and feels confident that this homework score will be at least a 90. Predict what will happen to her mean absolute deviation if she is correct:
.
Tammy was correct. She earned a 92! The new mean absolute deviation of her homework scores now that they are 68, 76, 70, 74, and 92 is:
.
.
Tammy worked hard on yesterday’s assignment and feels confident that this homework score will be at least a 90. Predict what will happen to her mean absolute deviation if she is correct:
.
Tammy was correct. She earned a 92! The new mean absolute deviation of her homework scores now that they are 68, 76, 70, 74, and 92 is:
.
Answers
GPT-4o mini
To find the mean absolute deviation (MAD) of Tammy's homework scores, we first need to calculate the mean of her initial scores (68, 76, 70, and 74).
1. **Calculate the mean of the initial scores:**
\[
\text{Mean} = \frac{68 + 76 + 70 + 74}{4} = \frac{288}{4} = 72
\]
2. **Calculate the absolute deviations from the mean:**
- For 68: \( |68 - 72| = 4 \)
- For 76: \( |76 - 72| = 4 \)
- For 70: \( |70 - 72| = 2 \)
- For 74: \( |74 - 72| = 2 \)
3. **Calculate the mean absolute deviation:**
\[
\text{MAD} = \frac{4 + 4 + 2 + 2}{4} = \frac{12}{4} = 3
\]
**So, the mean absolute deviation of her scores is 3.**
Now, let's predict what happens to her mean absolute deviation if she scores a 90:
To see the effect of adding a score of 90, we'll calculate the new mean and MAD with the five scores (68, 76, 70, 74, and 92).
1. **Calculate the new mean:**
\[
\text{New Mean} = \frac{68 + 76 + 70 + 74 + 92}{5} = \frac{380}{5} = 76
\]
2. **Calculate the absolute deviations from the new mean:**
- For 68: \( |68 - 76| = 8 \)
- For 76: \( |76 - 76| = 0 \)
- For 70: \( |70 - 76| = 6 \)
- For 74: \( |74 - 76| = 2 \)
- For 92: \( |92 - 76| = 16 \)
3. **Calculate the new mean absolute deviation:**
\[
\text{New MAD} = \frac{8 + 0 + 6 + 2 + 16}{5} = \frac{32}{5} = 6.4
\]
**So, the new mean absolute deviation of her homework scores now that they are 68, 76, 70, 74, and 92 is 6.4.**
1. **Calculate the mean of the initial scores:**
\[
\text{Mean} = \frac{68 + 76 + 70 + 74}{4} = \frac{288}{4} = 72
\]
2. **Calculate the absolute deviations from the mean:**
- For 68: \( |68 - 72| = 4 \)
- For 76: \( |76 - 72| = 4 \)
- For 70: \( |70 - 72| = 2 \)
- For 74: \( |74 - 72| = 2 \)
3. **Calculate the mean absolute deviation:**
\[
\text{MAD} = \frac{4 + 4 + 2 + 2}{4} = \frac{12}{4} = 3
\]
**So, the mean absolute deviation of her scores is 3.**
Now, let's predict what happens to her mean absolute deviation if she scores a 90:
To see the effect of adding a score of 90, we'll calculate the new mean and MAD with the five scores (68, 76, 70, 74, and 92).
1. **Calculate the new mean:**
\[
\text{New Mean} = \frac{68 + 76 + 70 + 74 + 92}{5} = \frac{380}{5} = 76
\]
2. **Calculate the absolute deviations from the new mean:**
- For 68: \( |68 - 76| = 8 \)
- For 76: \( |76 - 76| = 0 \)
- For 70: \( |70 - 76| = 6 \)
- For 74: \( |74 - 76| = 2 \)
- For 92: \( |92 - 76| = 16 \)
3. **Calculate the new mean absolute deviation:**
\[
\text{New MAD} = \frac{8 + 0 + 6 + 2 + 16}{5} = \frac{32}{5} = 6.4
\]
**So, the new mean absolute deviation of her homework scores now that they are 68, 76, 70, 74, and 92 is 6.4.**