問48
頻出度★★★
あるシステムの設計工程における設計書作成の予定所要工数，及び現在の各設計書の進捗率は表のとおりである。予定どおりの所要工数で完了まで進むものとして，すべての設計書の完了を100%としたとき，現在の全体の進捗率（%）は幾らか。
| 予定所要工数（時間） | 現在の進捗率（%） | |
|---|---|---|
| 外部設計書 | 500 | 100 |
| 内部設計書 | 700 | 50 |
| プログラム設計書 | 900 | 30 |
平成21年度 春期 ITパスポート試験 問48
マネジメント系プロジェクトマネジメント › プロジェクトマネジメント
This question's explanation and your answers so far.
解説
問 48
Incorrectア
40% is a value that does not come out of any calculation on the table. At most it corresponds to the remainder of the 60% obtained by taking a simple average of the three progress rates (100−60=40), but the question asks for the current progress rate, not the proportion of remaining work, and the simple average itself is a wrong calculation that ignores the weight of the effort. It is far away from the correct weighted average of 53.3%.
Incorrectイ
47% is the flip side of the correct progress rate of 53%, that is, the proportion of work still remaining (100−53≈47). Adding up the effort not yet finished gives 700×50%+900×70%=350+630=980 hours, and 980÷2100≈46.7%, which produces exactly this value. The question asks for “the current overall progress rate”, meaning the completed share, so the answer is 53%, not 47%.
- ウ
正解 The correct answer is ウ (53%). The overall progress rate is obtained as a weighted average that uses the amount of work (the planned required effort) as the weight. First, the denominator, the total amount of work, is 500+700+900=2100 hours. Next, the numerator, the work completed so far, is calculated for each design document as “planned required effort × progress rate”: external design document 500×100%=500 hours, internal design document 700×50%=350 hours, program design document 900×30%=270 hours, giving a total of 500+350+270=1120 hours. The overall progress rate is therefore 1120÷2100=0.5333…, that is about 53.3%, which corresponds to 53, choice ウ. This also matches the intuition that the program design document with the largest effort (900 hours) has advanced only 30%, so the whole work stays just barely above 50%.
Incorrectエ
60% is the value obtained by taking the plain simple average of the three progress rates: (100+50+30)÷3=60. However, the planned required effort differs by document, at 500 / 700 / 900 hours, so a simple average that ignores the weight of the work amount cannot be used. The delay of the program design document with the largest effort is then not reflected properly, and progress looks higher than it really is. This is a typical mistake.
ここがポイント
- The overall progress rate is obtained as a weighted average using effort as the weight. Overall progress rate = Σ (planned effort of each task × progress rate of each task) ÷ Σ (planned effort of each task). Here it is 1120÷2100≈53%.
- When the tasks differ in size, taking a simple average of the progress rates (60% in this question) is wrong. The delay of a large task gets diluted, so you must weight the values by effort (or by cost, effort share, or a similar weight). At the same time, check what the question is actually asking, so that you do not mistake the flip side of the value (100 − progress rate = the proportion of remaining work) for the answer.
用語