Is the average time an activity will take if it were to be repeated on large number of times?
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A theorem that describes the result of repeating the same experiment a large number of times Show
What is the Law of Large Numbers?In statistics and probability theory, the law of large numbers is a theorem that describes the result of repeating the same experiment a large number of times. The large numbers theorem states that if the same experiment or study is repeated independently a large number of times, the average of the results of the trials must be close to the expected value. The result becomes closer to the expected value as the number of trials is increased. The law of large numbers is an important concept in statistics because it states that even random events with a large number of trials may return stable long-term results. Note that the theorem deals only with a large number of trials while the average of the results of the experiment repeated a small number of times might be substantially different from the expected value. However, each additional trial increases the precision of the average result. Example of Law of Large NumbersThe simplest example of the law of large numbers is rolling the dice. The dice involves six different events with equal probabilities. The expected value of the dice events is: If we roll the dice only three times, the average of the obtained results may be far from the expected value. Let’s say you rolled the dice three times and the outcomes were 6, 6, 3. The average of the results is 5. According to the law of the large numbers, if we roll the dice a large number of times, the average result will be closer to the expected value of 3.5. Law of Large Numbers in FinanceIn finance, the law of large numbers features a different meaning from the one in statistics. In the business and finance context, the concept is related to the growth rates of businesses. The law of large numbers states that as a company grows, it becomes more difficult to sustain its previous growth rates. Thus, the company’s growth rate declines as it continues to expand. The law of large numbers may consider different financial metrics such as market capitalization, revenue, and net income. Practical ExampleLet’s consider the following example. Company ABC’s market capitalization is $1 million while Company XYZ’s market capitalization is $100 million. Company ABC experiences a significant growth of 50% per year. For ABC, the growth rate is easily attainable since its market capitalization only grows by $500,000. For Company XYZ, that growth rate is almost impossible because it implies that its market capitalization should grow by $50 million per year. Note that the growth of Company ABC will decline over time as it continues to expand. Related ReadingsCFI is the official provider of the Financial Modeling and Valuation Analyst (FMVA)™ certification program, designed to transform anyone into a world-class financial analyst. To keep learning and developing your knowledge of financial analysis, we highly recommend the additional CFI resources below:
What Is a PERT Chart?A PERT chart is a network diagram used in the Program Evaluation Review Technique (PERT) to represent a project’s timeline. It allows project managers to estimate the duration of projects based on the analysis of task sequences. PERT charts are used by project managers to create realistic schedules by coordinating activities and estimating their duration by assigning three time estimates for each (optimistic, most likely and pessimistic). This makes PERT charts useful when planning projects where the duration of activities is uncertain. PERT Charts are more powerful when combined with online project scheduling software, and ProjectManager makes applying your PERT analysis simple. Sign up for a free 30 days trial today and make dynamic project schedules that update in real time as your team completes their tasks. It’s never been easier to make a schedule and deliver a project on time and under budget. What Is a PERT Chart Used for in Project Management?The PERT chart identifies the critical path to estimate the minimum amount of time that will be needed to execute all the tasks of a project. This is done by examining the breakdown of the project, estimating the duration of each activity, the dependencies between them and the order in which they must be completed. Simplify Complex ProjectsPERT charts help project managers get a handle on complex projects. They’re useful because they provide an estimation of how much time you’ll need to schedule the project and what resources will be required. The nature of the PERT chart and its breakdown structure helps to visualize the complexity of a project and the dependencies between each step in the process.  An example of a PERT chart for a project. Involve Multiple Departments & Subject Matter ExpertsA PERT chart also serves as a project management tool that pulls in data from every department working on the project. This helps project managers identify who is doing what, and provides clear responsibilities for those tasks. Strong communication is facilitated between departments, and the overall strategic goals of the organization are better aligned. Explore the HypotheticalAnother benefit of using a PERT chart is it allows project managers to create what-if scenarios. By mapping out the tasks, time and resources for a project, you can quickly see what is working and what is not. This saves a lot of time that would otherwise be wasted in revisions. This flexibility makes PERT charts useful in project management. Using PERT Charts & CPM in Project ManagementProject managers often use PERT charts along with the critical path method (CPM), which is a network analysis that discerns which tasks and activities must be completed to deliver a successful project. They’re used together when creating a project schedule, planning costs, scheduling resources and controlling a project to keep it on schedule. When combined, they result in a more conservative view of the duration of tasks and activities. Related: Free Project Scheduling Templates for Excel Pitfalls of a PERT ChartPERT charts are not a panacea to get your projects magically on track, though. Naturally, bad data-in will result in bad data-out. It’s important that the person conducting the PERT analysis has experience in the process. They’re also labor intensive, which some organizations might not have the time or money to invest in. Additionally, you just don’t build a PERT and call it a day. They require continuous reviews and updates to make sure they’re accurate. If you’re using a PERT chart template, you’ll have to create many versions of it. What Is PERT Chart Software?PERT chart software is used to help project managers better estimate the realistic duration of their project. PERT charts are a form of diagram, and can be built robustly using a dedicated PERT chart maker. A PERT chart software allows you to create PERT charts that are dynamic and easily updated, unlike a PERT chart template. PERT chart software is really a feature of a larger project management tool that takes the PERT diagram and imports it into a Gantt chart software. Now, the PERT chart can be the stepping stone to adding durations to your tasks, linking dependencies, setting milestones and assigning work to the team. Must-Have Features of PERT Chart SoftwareYou can use a PERT chart maker, and also invest in project management software, or you could get them all in one tool that has these essential features: Organize and Schedule TasksPERT charts give you an idea of how long the project should take, and a Gantt chart fine tunes that by collecting all your tasks on a project timeline. Estimate the duration of each task, set milestones to better track as you move from one phase to another and assign your team work. Link Tasks, Avoid BottlenecksGantt charts control tasks by linking dependent ones together. Some tasks can’t start or finish until another starts or finishes. If you don’t identify these during the planning stage, you might block the team when they’re executing their work. Linking dependencies keep you on track. Plan Your Project TimelineGantt charts are a manager’s go-to tool for scheduling projects. They manage all your tasks, subtasks, resource costs associated with the tasks and even planned starts and finishes. Then, by setting a baseline, you save that data and can compare it against your actual progress. Automate CalculationThe critical path is an algorithm that is used to better schedule projects. The calculation is somewhat complex, and pulls you away from other important project duties. Some Gantt charts will automatically chart the critical path in your project, which saves time. See Project Metrics in Real-TimeDashboards are a collection of project metrics displayed in graphs and charts that give you a bird’s-eye view of the project’s performance. If you’re using online software, that data is delivered in real-time to give you a more accurate status report on progress. Make Data-Driven DecisionsThe PERT chart estimates, project reporting defines. Reports can be generated to show project variance, task and time progress, workload, costs and more. They provide accurate data to make better decisions and can be shared to keep your stakeholders updated. PERT Charts in Project ManagementA PERT chart is a project management chart that includes numbered nodes, directional arrows and divergent arrows that illustrate the minimum time and duration of activities. Directional arrows represent the activities, while nodes are milestones. Our PERT chart example will allow you to see these elements. As stated, the use of the PERT chart gives project managers a tool to estimate the time and resources needed to complete their project tasks, which is crucial during the initiation and planning phases. When it comes to starting a project, the early steps involve taking all those tasks you collected that lead to your final deliverable and organizing them in a schedule. Knowing the amount of time it’ll take to complete each task, especially the riskier ones, is fundamental for project managers. How to Make a PERT ChartUse a PERT chart in the planning phase of your project. Here are the steps in broad strokes before we get to our PERT chart example:
How to Calculate a PERT ChartBefore we create a PERT chart, it’s helpful to know how to calculate a project duration using the Program Evaluation and Review Technique. A PERT chart relies on the weighted average of three numbers that are based on the most pessimistic (P), the most optimistic (O) and the most likey (M) estimates for the project’s length.
Using the figures you come up with for P, O and M, calculate the equation: How to Use the PERT Chart FormulaUsing the optimistic, most likely, and pessimistic time estimates, you can use the PERT formula to calculate the expected duration of a task: (O + (4*M) + P) / 6 The result is a weighted average, which is an average from multiplying each element by a factor that reflects its importance. You can think of this as the expected time, though often the calculation will bend towards the pessimistic. The result of this formula will be the value that you’ll assign to the arrows in our PERT chart example. What Is the PERT Chart Standard Deviation?To determine the standard deviation of the estimated duration of an activity, subtract the pessimistic number from the optimistic one and divide the results by six. The larger your results, the less confidence you have in your estimate, and vice versa. (P-O) / 6 PERT Chart ExampleLet’s move these concepts from abstraction to reality. To better understand the power of a PERT chart in project management, let’s make one together. For our PERT chart example, we’ll create a project around building a website. The PERT chart will allow us to visualize our project’s activities and milestones to quickly uncover the critical path. Observe the PERT Chart example below, and we’ll walk through how we created it. PERT ChartOur Sample PERT Chart, ExplainedTo begin with our PERT example, we’re going to identify all the activities that make up the project and determine the immediate predecessors for each. We’ll list them as shown in the table above, known as the activity list. Milestones are the nodes in our PERT chart, and they’re the outcome of each activity. Next, we figure out how long all the activities to get to our milestones will take. The amount of time you estimate with the PERT chart formula should be added to the arrows as shown in our PERT chart example. We used weeks as our time unit, but it could be days or months, depending on your project. Once we have a time estimate for each task, we can draw our network diagram. We start with the first node which is the “kick off meeting” in our example. Then we represent the initial activities with arrows and connect them to their corresponding milestone nodes. We continue the process until we get to the final milestone node of our project. With the completed chart, it becomes clear which activities are critical to delivering the project on time. These are represented by the white arrows. Once the critical path is determined, you can easily refer to it as a roadmap to keep your project on track! PERT Chart VideoAll of these explanations can be a bit hard to understand by text. If you’re more of a visual learner, watch project management expert Jennifer Bridges, PMP, as she walks you through the steps of creating a PERT chart in this short tutorial video. Glossary of Terms Related to PERT ChartsThese concepts will allow you to understand the Program Evaluation and Review Technique and the anatomy of a PERT chart:
History of PERT ChartsThe Program Evaluation and Review Technique (PERT) has been around for a while in project management, but it was, in fact,
developed by the U.S. Navy. In 1957, the Special Projects Office created the PERT chart to assist in its Polaris nuclear submarine project. PERT diagrams and the critical path method came about at roughly the same time, growing from the scientific management founded by Frederick Taylor, also called Taylorism, which was later refined by Henry Ford. But the use of the term critical path comes from DuPont, which developed the method also in the late 1950s. What Is the Difference Between a Gantt Chart and a PERT Chart?While both PERT charts and Gantt charts are visual tools used by project managers for project planning, they are not exactly the same thing. PERT charts, as detailed above, were developed to simplify planning and scheduling larger and complex projects. Gantt charts, on the other hand, are also a graphical depiction for planning and scheduling a project, which breaks down the project scope into tasks that populate a timeline. A Gantt chart can be used to build the project timeline, set task dependencies and show the duration of each task. There are other key differences, as well. For example, Gantt charts represent the project timeline with a bar chart. A PERT chart is more of a flowchart or network diagram. Gantt charts can be used on smaller projects, while PERT charts are for larger and more complex projects. The most salient difference is that a PERT chart is usually used before starting a project to figure out scheduling, while Gantt charts tend to follow into the project, highlighting scheduling constraints. Gantt chart software can be used by project managers when executing the project as well as when planning because tasks’ start and end dates can be edited. Gantt charts reveal how long each task will take, show who on the team is responsible for those tasks and are a more transparent tool to track progress and keep track of tasks and resources. Pro Tip: A PERT chart is a great way to help you estimate simply and more accurately. Estimates can be overly optimistic or pessimistic, but using a PERT chart will find the most realistic estimate. What Is the Difference Between a PERT Chart and CPM?PERT charts and the Critical Path Method (CPM) both make use of network diagrams to estimate the duration of individual activities and projects, but they’re different project management techniques. For instance, the PERT diagram represents activities as arrows and milestones as nodes. While, on the other hand, the CPM diagram depicts activities as nodes. Also, a PERT chart offers the possibility of including three time estimates for activities which is not possible with CPM. This is because PERT was designed to plan projects with uncertain activity times, while CPM is used for projects where activity times are known. Using PERT Charts with ProjectManagerThe PERT chart is a tool that helps project managers plan and schedule. ProjectManager helps you take that PERT chart and apply it to managing your whole project with our online Gantt chart. It plans, schedules and works through the execution of the project. Our Gantt chart gives you control over every aspect of your schedule, from placing milestones, assigning team members and linking task dependencies. We easily link all four types of task dependencies — finish-to-start, finish-to-finish, start-to-finish and start-to-finish — so you can avoid bottlenecks later in the project. Unlike a PERT chart, our Gantt chart isn’t static. No matter how good your estimations, there will always be issues that pop up in a project. You can prepare for risk and mitigate it, but often the schedule will have to adapt to keep you on time. We have drag-and-drop editing to quickly and easily change start and due dates, which is then reflected throughout the software. That’s just the tip of the iceberg for our award-winning project management software. We can help you keep your projects and teams organized. See for yourself why tens of thousands of teams use our software to work more productively by starting your free 30-day trial. Start My Free Trial Is the estimate of the normal time the activity would take?Most likely time:
The most probable estimate of time which an activity may take for its completion under normal conditions. It is denoted by tm. This is the time estimate usually obtained by experienced engineers.
Is time estimate of an activity when everything is assumed to go well as per plan?Optimistic time, expressed as 'to',represents estimate of minimum possible time by which an activity can be completed assuming that everything is in order according to the plan and there can be only minimum amount of difficulty.
What are the 3 time estimates used in PERT?To perform PERT analysis, you need to provide three estimates of activity duration: a pessimistic estimate (tp), an optimistic estimate (to), and a modal estimate (tm). These three estimates are used to obtain a weighted average that is assumed to be a reasonable estimate of the activity duration.
What is PERT time estimate?PERT is used to estimate project duration or cost. PERT is a “weighted” average estimate technique. PERT is best used for planning to ensure accurate scope. PERT formula is an approximation of the Beta Distribution equation. PERT is determined using three points: Optimistic (O), Most Likely (M), and Pessimistic (P).
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