Question 32 asks what operations should be performed in areas labeled 'A' and 'B' in the flowchart in Figure 1 to calculate the average of 25 exam scores. Question 33 asks how the flowchart in Figure 2 should be modified to calculate the sum of even numbers from 0 to 100 (inclusive).

Applied MathematicsAlgorithmsFlowchartsAveragesSummation
2025/5/5

1. Problem Description

Question 32 asks what operations should be performed in areas labeled 'A' and 'B' in the flowchart in Figure 1 to calculate the average of 25 exam scores.
Question 33 asks how the flowchart in Figure 2 should be modified to calculate the sum of even numbers from 0 to 100 (inclusive).

2. Solution Steps

Question 32:
In Figure 1, the flowchart calculates the average of NN exam scores.
- The flowchart initializes I=1I = 1, N=25N = 25, and SUM=0SUM = 0.
- Inside the loop, it inputs the II'th exam score XX.
- At area A, the current exam score should be added to the running sum. Thus, the operation should be SUM=SUM+XSUM = SUM + X.
- The loop continues until I>NI > N.
- After the loop, area B calculates the average AVGAVG. Since the sum of the scores is stored in SUMSUM, and the number of scores is NN, the average is AVG=SUM/NAVG = SUM / N.
Question 33:
In Figure 2, the flowchart calculates the sum of numbers from 0 to
1
0

0. The flowchart initializes $SUM = 0$ and $I = 0$. The loop continues as long as $I \le 100$. Inside the loop, $SUM = SUM + I$ and $I = I + 1$. To calculate the sum of even numbers from 0 to 100:

- The initial value of II should be the first even number,

0. So changing $I=0$ to $I=2$ is wrong.

- The increment should be 2 to only add even numbers: I=I+2I = I + 2.
- The summation remains the same: SUM=SUM+ISUM = SUM + I. The number II is only even in this summation.

3. Final Answer

Question 32:
(1) Sum=Sum+x,Avg=Sum/NSum = Sum + x, Avg = Sum / N
Question 33:
(2) Change the increment statement 'I = I+1' into 'I = I+2'

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