Question

1st grade
2nd grade
3rd grade
4th grade
zero
add the first four grades then divide by four to calculate the grade average without a zero.
add all five grades then divide by five to calculate the grade average with a zero.
change the \0\ to a \50\ then add all five grades and divide by five to calculate the grade average with a 50 instead of a zero.
what effect did one \zero\ have on the average grades? how much did the letter grade change? (e.g., from an \a\ to a \c.\)
some teachers will let you turn in a late assignment for at least partial credit. how much did changing a \0\ with a partial credit of \50\ change the average grades?

Explanation:

Step1: Calculate average with zero

Let the first four grades be \(a = 96\), \(b = 84\), \(c = 88\), \(d = 92\) and the fifth - grade \(e = 0\). The sum of the five grades \(S_1=a + b + c + d+e=96 + 84+88 + 92+0=360\). The average \(A_1=\frac{S_1}{5}=\frac{360}{5}=72\).

Step2: Calculate average with 50

Replace \(e = 0\) with \(e = 50\). The sum of the five grades \(S_2=a + b + c + d+e=96 + 84+88 + 92+50=410\). The average \(A_2=\frac{S_2}{5}=\frac{410}{5}=82\).

Step3: Find the difference in averages

The difference \(\Delta A=A_2 - A_1=82 - 72 = 10\).

Answer:

The average grade increased by 10 when the grade was changed from 0 to 50.