Question

homework
1 89
2 90
3 91
4 92
5 93
6 94
7 45
8 96
9 97
10 98
11 99
12 100
average: 90.3
a.)
exams
1 85
2 96
average: 90.5
paper
78
final
92
grade
88.4
b.)
c.)
hw min: 45.0
d.)
new hw average:
new grade:
a.) compute the mean homework grade and the mean of the two exam grades, using the average function. format to one decimal place.
b.) compute the total grade for the class using the weighted average formula:
40%(exam avg.) + 15%(hw avg.) + 20%(paper) + 25%(final).
format as a number with one decimal place.
c.) your professor says that the lowest homework grade will be thrown out. calculate the lowest homework grade using the min function.
d.) re-compute a new homework average (hint: use sum and subtract the min). format to one decimal place.
re-compute a new grade for the class. format as a number with one decimal place.

Explanation:

Part a) (Already given, but let's verify)

Mean Homework Grade:

The homework grades are: 89, 90, 91, 92, 93, 94, 45, 96, 97, 98, 99, 100.
Number of homework grades \( n = 12 \).
Sum of homework grades: \( 89 + 90 + 91 + 92 + 93 + 94 + 45 + 96 + 97 + 98 + 99 + 100 \)
Calculate step - by - step:
\( 89+90 = 179 \); \( 179 + 91=270 \); \( 270+92 = 362 \); \( 362+93 = 455 \); \( 455+94 = 549 \); \( 549+45 = 594 \); \( 594+96 = 690 \); \( 690+97 = 787 \); \( 787+98 = 885 \); \( 885+99 = 984 \); \( 984+100 = 1084 \)
Mean \(=\frac{1084}{12}\approx90.3\) (matches the given value)

Mean of two exam grades:

Exam grades: 85, 96.
Number of exam grades \( n = 2 \).
Sum of exam grades: \( 85 + 96=181 \)
Mean \(=\frac{181}{2}=90.5\) (matches the given value)

Part b) (Already given, but let's verify)

Given:
Exam Avg \(= 90.5\), HW Avg \(= 90.3\), Paper \(= 78\), Final \(= 92\)
Weighted average formula: \( 0.4\times(\text{Exam Avg})+0.15\times(\text{HW Avg})+0.2\times(\text{Paper})+0.25\times(\text{Final}) \)
Substitute the values:
\( 0.4\times90.5+0.15\times90.3 + 0.2\times78+0.25\times92 \)
\( 0.4\times90.5 = 36.2 \); \( 0.15\times90.3=13.545 \); \( 0.2\times78 = 15.6 \); \( 0.25\times92 = 23 \)
Sum: \( 36.2+13.545 + 15.6+23=88.345\approx88.4\) (matches the given value)

Part c) (Already given, but let's verify)

Homework grades: 89, 90, 91, 92, 93, 94, 45, 96, 97, 98, 99, 100.
The minimum value among these is 45.0 (matches the given value)

Part d)

Step 1: Calculate the sum of original homework grades

We already found that the sum of original homework grades \( S = 1084 \)

Step 2: Subtract the minimum homework grade

Minimum homework grade \( \text{Min}=45 \)
New sum of homework grades \( S_{\text{new}}=S - \text{Min}=1084 - 45 = 1039 \)

Step 3: Calculate the new number of homework grades

Original number of homework grades \( n = 12 \), after removing one grade, \( n_{\text{new}}=12 - 1=11 \)

Step 4: Calculate the new homework average

New HW Average \(=\frac{S_{\text{new}}}{n_{\text{new}}}=\frac{1039}{11}\approx94.5\) (rounded to one decimal place)

Step 5: Calculate the new total grade

Using the weighted average formula: \( 0.4\times(\text{Exam Avg})+0.15\times(\text{New HW Avg})+0.2\times(\text{Paper})+0.25\times(\text{Final}) \)
Substitute the values:
Exam Avg \( = 90.5 \), New HW Avg \( = 94.5 \), Paper \( = 78 \), Final \( = 92 \)
\( 0.4\times90.5+0.15\times94.5+0.2\times78 + 0.25\times92 \)
\( 0.4\times90.5=36.2 \); \( 0.15\times94.5 = 14.175 \); \( 0.2\times78=15.6 \); \( 0.25\times92 = 23 \)
Sum: \( 36.2+14.175+15.6 + 23=88.975\approx89.0\) (rounded to one decimal place)

Answer:

s:

• New HW Average: \(\boldsymbol{94.5}\)
• New Grade: \(\boldsymbol{89.0}\)