Question

the data set 67, 72, 72, 78, 84, 89, 98 describes test grades in mrs. brights calculus class. the lowest - scoring student in mrs. brights class is allowed a retake, where her adjusted quiz grade would be the average of the original and retake quiz grades. the student scores a 79 on her retake quiz. what is the difference between the old and new class range? 0 5 12 26

Explanation:

Step1: Calculate the old range

The range is the difference between the maximum and minimum values.
Old maximum = 98, old minimum = 67.
Old range: \(98 - 67=31\)

Step2: Calculate the new minimum

The lowest - scoring student's original grade is 67. The adjusted grade is \(\frac{67 + 79}{2}=\frac{146}{2} = 73\)
New maximum = 98, new minimum = 73
New range: \(98 - 73=25\)

Step3: Calculate the difference between old and new range

Difference: \(31-25 = 6\)

Wait, there is a mistake above. Let's recalculate:

Step1: Calculate the old range

The range is the difference between the maximum and minimum values.
Old maximum \(M_{old}=98\), old minimum \(m_{old}=67\)
Old range \(R_{old}=M_{old}-m_{old}=98 - 67=31\)

Step2: Calculate the new minimum

The lowest - scoring student's original grade is \(67\). The adjusted grade is \(\frac{67 + 79}{2}=\frac{146}{2}=73\)
New maximum \(M_{new}=98\), new minimum \(m_{new}=73\)
New range \(R_{new}=M_{new}-m_{new}=98 - 73 = 25\)

Step3: Calculate the difference between old and new range

Difference \(D=R_{old}-R_{new}=31-25 = 6\)

Wait, no, check the problem again. The original data set is \(67,72,72,78,84,89,98\). After the adjustment, the data set becomes \(73,72,72,78,84,89,98\) (since we replace \(67\) with \(73\)).

Step1: Calculate the old range

The formula for the range \(R=\text{Max}-\text{Min}\)
For the old data set \(67,72,72,78,84,89,98\), \(\text{Max}_{old}=98\), \(\text{Min}_{old}=67\)
\(R_{old}=98 - 67=31\)

Step2: Calculate the new minimum

The adjusted grade of the lowest - scoring student: \(\frac{67 + 79}{2}=73\)
For the new data set \(73,72,72,78,84,89,98\), \(\text{Max}_{new}=98\), \(\text{Min}_{new}=72\) (because \(72<73\))
\(R_{new}=98 - 72=26\)

Step3: Calculate the difference

\(D = R_{old}-R_{new}=31-26=5\)

Answer:

5