To determine where Lauren made her error, we need to carefully review the steps given and the correct values for medians and interquartile ranges (IQRs).
### Step-by-Step Solution:
1. Given Information:
- The median for chemistry is 85.
- The median for biology is 80.
2. Step 2: Find the difference in the medians.
- Lauren's calculation: [tex]\(80 - 70 = 10\)[/tex]
- Correct calculation: The medians are 85 (chemistry) and 80 (biology), so the difference should be:
[tex]\[ 85 - 80 = 5 \][/tex]
3. Step 3: Find the interquartile range (IQR) for chemistry and biology.
- Lauren's calculation for chemistry IQR: [tex]\(85 - 80 = 5\)[/tex]
- Lauren's calculation for biology IQR: [tex]\(85 - 80 = 5\)[/tex]
- Correct calculation:
- Chemistry IQR: [tex]\(85 - 60 = 25\)[/tex]
- Biology IQR: [tex]\(80 - 60 = 20\)[/tex]
4. Step 4: Find the difference in the IQRs.
- Lauren’s calculation: [tex]\(10 - 5 = 5\)[/tex]
- Correct difference using correct IQRs:
[tex]\[ 25 - 20 = 5 \][/tex]
### Conclusion:
Lauren's calculations contained multiple inaccuracies:
- In Step 2, the median difference should be [tex]\(5\)[/tex] (not [tex]\(10\)[/tex]).
- In Step 3, the correct IQRs were not used.
Consequently, the statement:
"Lauren made her first error in step 3 because she should have used [tex]\(85-60 = 25\)[/tex] for chemistry and [tex]\(80-60 = 20\)[/tex] for biology."
best explains Lauren’s error. This shows Lauren needed to correctly calculate the interquartile ranges for both subjects as the subtraction from the median.
Thus, Lauren’s first error indeed occurred in step 3 as described. This is our correct answer.
