--- title: "Bar chart; expected time and variance" subject: "Project Engineering" chapter: 3 key: "semester_7/project_engineering:bar-chart-draw-adv-te-variance" source: https://www.bctengineer.com/q/semester_7/project_engineering/bar-chart-draw-adv-te-variance site: BCT Engineering --- # Bar chart; expected time and variance Project Engineering · Chapter 3: Project Planning and Scheduling - Asked in: 2065 Shrawan (old course), 8 marks - Video: [What is the probability that a project will finish early or late (PERT)](https://www.youtube.com/watch?v=dOWQDAcYhPo) — Engineer4Free - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/project_engineering/bar-chart-draw-adv-te-variance - Whole chapter: https://www.bctengineer.com/md/semester_7/project_engineering/chapter-3 ## Question Draw a bar chart and explain its advantages and disadvantages. Also find te and variance when to, tm and tp are 6, 8, 12. ## Short answer A bar chart shows activities as horizontal bars on a time scale; it is simple and shows start, finish and overlap, but not logical dependence, critical path or float. For to=6, tm=8, tp=12, te=(6+4*8+12)/6=8.33 time units and variance=((12-6)/6)^2=1. ## Answer #### Bar chart A **bar chart** shows each activity as a horizontal bar on a time scale; the length of the bar is the duration. Example: house project (weeks). ```text 0 4 8 12 16 20 24 (wk) +------------------------ A Site clearing |# B Excavation | ## C Foundation | ### D Plinth beam | ## E Walls+columns | ##### F Roof slab | ### G Plumb/electric| ### H Plastering | ### I Floor,doors | ### J Painting | ## +------------------------ ``` #### Advantages - Simple to prepare, read and understand, even for non-technical persons. - Shows start, finish, duration and overlap of activities on a time scale. - Cheap and quick; needs no special training. - Good for presenting the summary to top management and site staff. - Progress can be marked on the bars and compared with the plan. - Useful for resource scheduling on a time scale. #### Disadvantages - Does not show the logical dependence between activities, so the effect of a delay on other activities is not seen. - Critical activities and float are not shown, so the manager cannot say where attention is needed. - Not suitable for large and complex projects; the chart becomes crowded. - Difficult to update; any change in logic needs redrawing. - Durations are single-point values; uncertainty is not considered. - Does not show resource or cost relations. #### Expected time and variance (PERT) Given: optimistic time $t_o = 6$, most likely time $t_m = 8$, pessimistic time $t_p = 12$. $$ \begin{aligned} t_e &= \frac{t_o + 4t_m + t_p}{6} = \frac{6 + 4(8) + 12}{6} = \frac{50}{6} = 8.33 \\ \sigma &= \frac{t_p - t_o}{6} = \frac{12 - 6}{6} = 1 \\ \text{Variance} &= \sigma^2 = 1^2 = 1 \end{aligned} $$ **Answer: $t_e = 8.33$ and variance $= 1$** (standard deviation 1). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the length of a bar represent? A. The cost of the activity B. The duration of the activity C. The float of the activity D. The probability of the activity Answer: B. Each bar is drawn on a time scale; length equals duration. (Key point: Bar chart) 2. Which is a disadvantage of a bar chart? A. It cannot be read by non-technical people B. It is expensive to prepare C. It does not show dependence between activities D. It cannot show start dates Answer: C. No logic is shown, so the effect of delay on others is unclear. (Key point: Disadvantage) 3. For to = 6, tm = 8, tp = 12, what is te? A. 8.33 B. 8.67 C. 9.00 D. 8.00 Answer: A. te = (6 + 4x8 + 12)/6 = 50/6 = 8.33. (Key point: Expected time) 4. What is the variance for these estimates? A. 6 B. 1 C. 2 D. 36 Answer: B. sigma = (12 - 6)/6 = 1, so variance = sigma^2 = 1. 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