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SECTION 03 / 15
Below average: finish one pass before filtering
On this page 3 headings
We want the students whose Mathematics mark is below the average of the whole class. A running average changes whenever another card is read. Deciding permanently from that unfinished average can give the wrong answer.
REAL COURSE DATA · FOLLOW THE PROCEDURE
Find Mathematics marks below the final average
Read the current record, check the explanation, and watch the variables. Use Back to revisit any step.
Ready
What we remember
- Processed
- 0
Start at the first step. Watch the current row and the values we remember.
Pass 1 computes; pass 2 selects
Sum = 0
Count = 0
for each row X in Scores {
Sum = Sum + X.Mathematics
Count = Count + 1
}
if (Count == 0) { report "No average"; stop }
Average = Sum / Count
for each row X in Scores {
if (X.Mathematics < Average) { record X.CardNo }
}Our 30 cards sum to 2,171, so the exact average is 2171/30 ≈ 72.3667. For integer marks, 72 is below this average and 73 is above it. Compare with the unrounded average, even when the display is rounded.
| Meaning | Result |
|---|---|
| Below-average IDs | 0, 1, 2, 3, 5, 9, 10, 12, 13, 17, 18, 19, 22, 24, 29 |
| Number below average | 15 |
| Visits for two full passes | 30 + 30 = 60 |
Two passes are not nested loops
The first loop ends before the second begins. We do not scan all 30 cards again inside each visit. Both passes may read the data without changing it; with physical piles, restore the cards before pass 2.
Below average does not always mean half
For the tiny example 50, 50, 50, 100, the average is 62.5 and three of four values are below it. If all values are equal, none is strictly below average. The result 15 out of 30 is a property of our supplied marks, not a general law.
Try it yourself
Why can a running average misclassify an earlier card?
Show explained answer
A later value can move the average up or down. An earlier value may cross the new threshold.
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Does a Mathematics mark of 72 pass the below-average test here?
Show explained answer
Yes. 72 < 2171/30.
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Are the two loops one inside the other?
Show explained answer
No. They run sequentially: finish pass 1, then start pass 2.
Try it yourself
What if Count is zero?
Show explained answer
Do not divide by zero. Report that there is no average.
Try it yourself
How many of 50,50,50,100 lie below their mean?
Show explained answer
Three. Their mean is 62.5.