Updated November 14, 2018
Marek Uliasz/iStock/Getty Images
Updated November 14, 2018
Although some business owners may be wary of using statistics, these equations can help you understand your company better. For example, understanding the three-sigma rule of thumb can help you make specific calculations or generally identify outliers in your business. However, you must learn to use it correctly for this equation to be effective.
What is 3 Sigma?
Three sigma is a calculation that comes from statistics. Researchers and statisticians use this calculation to identify outliers in data and adjust their findings accordingly. They do this because even well-controlled environments can yield results for which a study doesn't account.
For example, consider a prescription medication trial. If most patients on the new medicine saw improvements within a certain range, but one patient had an incredible change in their condition, it's likely that something else influenced this patient, not the drug in the study.
3 Sigma in Business
In business, you can apply the three-sigma principle to your analysis. For example, you may want to see how much your store makes on a given Friday. If you use three sigma, you may find that Black Friday is far outside the normal range. You may then decide to remove that Friday from your calculations when you determine how much the average Friday nets at your store.
You can also use three sigma to determine if your quality control is on target. If you determine how many defects your manufacturing company has per million units, you can decide if one batch is particularly faulty or if it falls within the appropriate range.
Generally, a three-sigma rule of thumb means 66,800 defects per million products. Some companies strive for six sigma, which is 3.4 defective parts per million.
Terms You Should Know
Before you can accurately calculate three sigma, you have to understand what some of the terms mean. First is 'sigma.' In mathematics, this word often refers to the average or mean of a set of data.
A standard deviation is a unit that measures how much a data point strays from the mean. Three sigma then determines which data points fall within three standard deviations of the sigma in either direction, positive or negative.
You can use an 'x bar' or an 'r chart' to display the results of the calculations. These graphs help you further decide if the data you have is reliable.
Make Your Calculations
Once you understand the purpose of the exercise and what the terms mean, you can get out your calculator. First, discover the mean of your data points. To do this, simply add up each number in the set and divide by the number of data points you have.
For example, assume the data set is 1.1, 2.4, 3.6, 4.2, 5.3, 5.5, 6.7, 7.8, 8.3 and 9.6. Adding up these numbers gives you 54.5. Since you have ten data points, divide the total by ten and the mean is 5.45.
Next, you need to find the variance for your data. To do this, subtract the mean from the first data point. Then, square that number. Write down the square you get, then repeat this method for each data point. Finally, add the squares and divide that sum by the number of data points. This variance is the average distance between the points and the mean.
Using the previous example, you would first do 1.1 - 5.45 = -4.35; squared, this is 18.9225. If you repeat this, add the sums and divide by ten, you find the variance is 6.5665. If you want, you can use an online variance calculator to do this part for you.
To find the standard deviation, calculate the square root of the variance. For the example, the square root of 6.5665 is 2.56 when rounded. You can use online calculators or even the one on your smartphone to find this.
Finally, it's time to find the three sigma above the mean. Multiply three by the standard deviation, then add the mean. So, (3x2.56) + 5.45 = 13.13. This is the high end of the normal range.
To find the low end, multiply the standard deviation by three and then subtract the mean. (3x2.56) - 5.45 = 2.23. Any data that is lower than 2.3 or higher than 13.13 is outside the normal range. For this example, 1.1 is an anomaly.
- Marek Uliasz/iStock/Getty Images
Im making a browser based PHP game and in my database for the players it has a record of that players total EXP or experience.
What i need is a formula to translate that exp into a level or rank, out of 100.
So they start off at level 1, and when they hit say, 50 exp, go to level 2, then when they hit maybe 125/150, level 2.
Basically a formula that steadily makes each level longer (more exp)
Can anyone help? I'm not very good at maths :P
divibisan6,61899 gold badges1818 silver badges3535 bronze badges
user880356user880356
7 Answers
Many formulas may suit your needs, depending on how fast you want the required exp to go up.
In fact, you really should make this configurable (or at least easily changed in one central location), so that you can balance the game later. In most games these (and other) formulas are determined only after
playtesting
and trying out several options.Here's one formula: First level-up happens at 50 exp; second at 150exp; third at 300 exp; fourth at 500 exp; etc. In other words, first you have to gather 50 exp, then 100 exp, then 150exp, etc. It's an Arithmetic Progression.
For levelup
X
then you need 25*X*(1+X)
exp.Added: To get it the other way round you just use basic math. Like this:
That's a standard Quadratic equation, and you can solve for X with:
Now, since we want both X and Y to be greater than 0, we can drop one of the answers and are left with:
So, for example, if we have 300 exp, we see that:
Now, this is the 3rd levelup, so that means level 4.
Vilx-Vilx-62.9k7373 gold badges239239 silver badges380380 bronze badges
If you wanted the following:
- Level 1 @ 0 points
- Level 2 @ 50 points
- Level 3 @ 150 points
- Level 4 @ 300 points
- Level 5 @ 500 points etc.
An equation relating experience (X) with level (L) is:
To calculate the level for a given experience use the quadratic equation to get:
This simplifies to:
Then round down using the floor function to get your final formula:
Where L is the level, and X is the experience points
MikeMike1,82133 gold badges2121 silver badges3434 bronze badges
It really depends on how you want the exp to scale for each level.Let's say
This means you have a geometric progression The Xp required to complete level n would be
In my example base is the inital 50 xp and Q is 2 (ratio).
The parent trap (1998 9xmovies. Identical twins Annie and Hallie, separated at birth and each raised by one of their biological parents, later discover each other for the first time at summer camp.
Provided a player starts at lvl1 with no xp:
and so forthThe total xp a player has when he gets a new level up would be:
In your case you already know how much xp the player has. For a ratio of 2 the formula gets simpler:
to find out the level for a given xp amount all you need to do is apply a simple formula
But with a geometric progression it will get harder and harder and harder for players to level.
To display the XP required for next level you can just calculate total XP for next level.
Check start of the post:to get from lvl1 -> lvl2 you need 50 xplvl2 ->lvl3 100xp
to get from lvl x to lvl(x+1)you would need
SleepersonSleeperson
Google gave me this:
It is supposed the be the formula that RuneScape uses, you might me able to modify it to your needs.Example output:
DirkZzDirkZz78922 gold badges88 silver badges1111 bronze badges
Here is a fast solution I used for a similar problem. You will likely wanna change the math of course, but it will give you the level from a summed xp.
NappingRabbitNappingRabbit1,72811 gold badge88 silver badges1818 bronze badges
I take it what you're looking for is the amount of experience to decide what level they are on? Such as:Level 1: 50expLevel 2: 100expLevel 3: 150exp ?
if that's the case you could use a loop something like:
This is as simple as I can make an algorithm for levels, I haven't tested it so there could be errors.
Let me know if you do use this, cool to think an algorithm I wrote could be in a game!
JohnJohn
The original was based upon a base of 50, thus the 25 scattered across the equation.
This is the answer as a real equation. Just supply your multiplier (base) and your in business.
Old Man WalterOld Man Walter
Not the answer you're looking for? Browse other questions tagged phpgame-development or ask your own question.
Site Planning - Phase I
Cut and Fill
Marianne Parsons
When planning the design and construction ofa building, architects and engineers must first consider the existingconditions of the site. Most often, the given site is not leveland must be modified before any construction can begin. So, thecut and fill process is typically one of the first constructionprocesses to take place on a site.
Without computer software to determine theamount of land to be added or removed, we can do simple calculationsto estimate the cut and fill volume of any site. First, the siteis divided into sections. Essentially, the site is 'sliced'into segments of land, at a specified fixed distance apart, sowe can look at each segment individually. Section cuts are drawnbased on the topography of the land in order to accurately representthe land that is being evaluated.
The topography map describes the existing slopesof the land, and allows us to draw site elevations in our sectioncuts.
Each line on the topography map representsa change in elevation of 10 feet. So the section at 0ft (the reddashed line above) looks like this in elevation:
Then, by removing the elevation lines, we getthe following section for the existing site elevation:
Now that we have two dimensional section cuts,we can estimate the area to be cut and filled in the site.On each section cut the desired land topography is representedas a 'cut line' overlaid on the line of the existingland topography. This gives us two lines on every section, andshows us how much of the existing area must be removed or added.Then, the area between these lines is calculated to find the cutand fill areas for each section.
The diagrams below represent the area betweenthe existing elevation line and the cut line. First, we mark theland that must be added to the site to achieve our desiredland topography. This area is marked 'fill.'
Next, we mark the land that must be removedfrom the site to achieve our desired land topography. This areais marked 'cut.'
By combining the two diagrams, we can see beginto estimate how much land area must be cut from the site, andhow much land area must be filled in the site to level the sitefor construction.
Now, once the section areas have been found,we must account for the additional length of the site (the landbetween the section cuts) to be able to estimate the volumeof the land cut or filled. Finally, after computing the necessaryvalues we are able to determine not only how much land must beremoved from or brought to the site, but also where that landmust be specifically taken from or brought to. Removing or addingland to any site is a costly process, so it is important thatour estimations be made as close to the existing conditions aspossible. Once we know how much land to cut or fill, and whereto cut and fill it, work can begin to properly level the siteand construct our building.
SITE AREAThe following activity uses the mathematicalconcepts of estimating area and volume to solve a realistic cutand fill problem. Each two-dimensional section cut is overlaidwith a grid to allow us to estimate the area between the existingelevation line and the cut line.
To estimate area, we can divide the area underthe curve into rectangles and then find the area of each rectangle.Refer to the diagram below for the process of drawing rectangles.Consistency in drawing the rectangles is very important to ensureproper balance between over and under estimation of area. Sinceall of the intervals are the same width of 10ft, the only estimatingthat you will need to do is with the height of each rectangle.For this exercise estimate the height to the nearest 2 1/2 feet(or 1/4 of the 10' X 10' square).
How To Calculate Formation Level In Profile Levelling
By removing the grid lines, it is easy to seethe areas of the rectangles that we will be estimating. Sincethese rectangles will represent and overestimation in some parts,and an underestimation in others, we will consistently draw ourrectangles and not worry about the area between the lines thatare missed.
The diagrams below represent two differentways rectangles can be drawn between the existing elevation lineand the cut line. The process of left and right estimation indicatethe direction in which the rectangles that meet the curve andare drawn.
SITE VOLUME
To estimate the volume, we use the area thathas been determined (as width and height) and then multiply bythe distance between each section (depth). Note that the firstand last section is on the site boundary. Notice also that theseboundary sections only have a volume on one of their sides.The remaining sections between the boundaries have land volumeon each side. See the diagram below. The solid lines referto our section cuts, and the dashed lines refer to the midpointbetween the section cuts. The volume for section cut 0ft is shadedbelow.
ESTIMATE THE AREA Download wild force sub indo batch.
1. Use the smaller grid lines at 10 feet toestimate the amount of land area that must be cut or filled foreach site section. Identify and label the areas of thesection that are to be cut or filled. Be sure to include the properunits in each of your answers.
a)
b)
c)
d)
e)
2. How would the area estimates change if wechose to divide the site sections into 1 foot increments, as opposedto the 10 foot increments used above? Which grid size would producean area estimate closer to the actual area of our site?
ESTIMATE THE VOLUME
1. Assuming our site has boundary lines atsection cut 0ft and at section cut 100ft, evaluatethe volume of land that must be cut or filled for each of thefive sections. Use the corresponding areas you found for eachsection in question 1. Think about how you would determine thesite depth to find volume? Use the image on page 2 to visualizethe volume of the land. Be sure to include the proper units ineach of your answers.
a) section 0ft
total cut volume:
total fill volume:
b) section 25ft
total cut volume:
total fill volume:
How To Calculate Design Formation Levels
c) section 50ft
total cut volume:
total fill volume:
d) section 75ft
total cut volume:
total fill volume:
e) section 100ft
total cut volume:
total fill volume:
2. Now, write a general expression for thevolume of land at a boundary line in terms of area.(i.e. Volume = Area * _____ ft). Briefly explain your answer.
Write a general expression for the volume ofland at section cut that is not a boundary linein terms of area. (i.e. Volume = Area * _____ ft). Briefly explainyour answer.
3. How would the estimates change if you choseto cut the site into ten 10ft sections rather than four 25ft sections?How would this affect our area estimate for each cut section asrelated to the actual site conditions?
ESTIMATE THE COST1. As site developers, we must figure out howmuch land will be moved on our site. By finding the sum of volumeto cut, and the sum of volume to fill, we can use the differenceto determine whether we need to add or remove land from our site.
a) What is the sum of the volume of land that must be cut from the site?
b) What is the sum of the volume of land that must be filled on the site?
c) What is the total volume of land that must be added or removed from the entire site?
2. Finally, to develop our site we are requiredto add or remove the volume of land calculated in question 1cabove. To move this land, we must hire dump trucks. Therefore,it is important for us to know how many dump truck loads willbe required to reasonably estimate the cost to level the site.
a) If the dimensions of a dump truck bed are 10 feet high, 8 feet wide, and 15 feet long, how many cubic feet of land can one dump truck carry?
b) How many dump truck loads are required to level our site?
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3. To remove a dump truck load from a site,the cost is $50. However, to add land to our site, the cost is$100 per load- $50 for transportation, and $50 to purchase theadditional land.
a) What is the total cost for adding/removing land from our site?
b) As a site planner, we would like to offer the client recommendation on how to reduce this cost. What practical recommendations can be made to lower our cost? Why?
Click below to use GSP filesfor this activity:section cuts: 0ft, 25ft, 50ft, 75ft, 100ft
Returnto Essay 3 - Site Planning Activities Updated September 26, 2017
Updated September 26, 2017
Many employers create salary ranges or grades used to assign compensation to individual jobs within the organization. The salary range allows you the ability to recruit employees of varying abilities and allows for salary increases for employees already holding positions. Ranges are also used in budgeting and planning. Salary ranges are often dictated by the employment market and the region in which your company does business.
Assign each job title a salary range. You can maintain your own organization's ranges based on budget.
Set a high and low salary for each range. Ranges can be reused for more than one job type.
Calculate the midpoint in the range. This is done by adding the low salary to the high salary and dividing by 2.
Cut your salary range into quarters or 'Quartiles.' You already have two sections from the midpoint calculation in Step 3. Find the quarter points between the low salary, midpoint and high salary. You now have 4 ranges of salaries. Quartiles are numbered from one to four based on low to high salary range.
Compare the employee's salary to the quartiles. If the salary falls within one of the quartile ranges, the number of that quartile is the position in range.