How to Estimate Standard Deviations (SD)

How to Estimate Standard Deviations (SD) The standard deviation and range are both measures of the spread of a data set. Each number tells us in its own way how spaced out the data are, as they are both a measure of variation.  Although there is not an explicit relationship between the range and standard deviation, there is a rule of thumb that can be useful to relate these two statistics.  This relationship is sometimes referred to as the range rule for standard deviation. The range rule tells us that the standard deviation of a sample is approximately equal to one-fourth of the range of the data. In other words s (Maximum – Minimum)/4. This is a very straightforward formula to use, and should only be used as a very rough estimate of the standard deviation. An Example To see an example of how the range rule works, we will look at the following example. Suppose we start with the data values of 12, 12, 14, 15, 16, 18, 18, 20, 20, 25. These values have a mean of 17 and a standard deviation of about 4.1. If instead we first calculate the range of our data as 25 – 12 13 and then divide this number by four we have our estimate of the standard deviation as 13/4 3.25. This number is relatively close to the true standard deviation and good for a rough estimate. Why Does It Work? It may seem like the range rule is a bit strange. Why does it work? Doesn’t it seem completely arbitrary to just divide the range by four? Why wouldn’t we divide by a different number? There is actually some mathematical justification going on behind the scenes. Recall the properties of the bell curve and the probabilities from a standard normal distribution. One feature has to do with the amount of data that falls within a certain number of standard deviations: Approximately 68% of the data is within one standard deviation (higher or lower) from the mean.Approximately 95% of the data is within two standard deviations (higher or lower) from the mean.Approximately 99% is within three standard deviations (higher or lower) from the mean. The number that we will use has to do with 95%. We can say that 95% from two standard deviations below the mean to two standard deviations above the mean, we have 95% of our data. Thus nearly all of our normal distribution would stretch out over a line segment that is a total of four standard deviations long. Not all data is normally distributed and bell curve shaped. But most data is well-behaved enough that going two standard deviations away from the mean captures nearly all of the data. We estimate and say that four standard deviations are approximately the size of the range, and so the range divided by four is a rough approximation of the standard deviation. Uses for the Range Rule The range rule is helpful in a number of settings. First, it is a very quick estimate of the standard deviation. The standard deviation requires us to first find the mean, then subtract this mean from each data point, square the differences, add these, divide by one less than the number of data points, then (finally) take the square root. On the other hand, the range rule only requires one subtraction and one division. Other places where the range rule is helpful is when we have incomplete information. Formulas such as that to determine sample size require three pieces of information: the desired margin of error, the level of confidence and the standard deviation of the population we are investigating. Many times it is impossible to know what the population standard deviation is. With the range rule, we can estimate this statistic, and then know how large we should make our sample.

Keeping a Writers Notebook

Keeping a Writers Notebook Keeping a Writers’ Notebook Keeping a Writers’ Notebook By Ali Hale If you’ve ever had aspirations towards fiction-writing, you’ve doubtlessly heard the advice to keep a notebook on you at all times, to jot down those elusive flashes of brilliance that come at the most inopportune moments. It’s definitely a good idea to have pen and paper to hand as much as possible – however, the discipline of keeping a writers’ notebook means more than just scribbling a few words when inspiration strikes. Writing every day One of the best uses for your notebook is to get into the habit of writing every single day. There are lots of different ways to approach this; some which have worked for me (not all at once) are: Write first thing in the morning Spend five minutes writing at some point in the morning, and five minutes in the afternoon Write just before going to bed Jot down some notes before starting on your â€Å"proper† writing session of the day Of course there’ll be days when you feel uninspired, when you have nothing you want to write about, or when you’re hectically busy. But if you’re going to stick with writing fiction long-term, it needs to become part of your daily life. What do you write about? Don’t be prescriptive about what goes in your notebook. Some people find it best to work in a deliberately â€Å"scrappy† book, so that they don’t feel constrained to only write down gems of wisdom – yes, moleskin notebooks may be hugely popular, but a 99 cent pad will be just as good a repository for your ideas. Some of the many types of writing filling my notebook are: To-do lists for writing sessions or writing days There’s a great sense of satisfaction in ticking things off or scoring them out. If a to-do list makes you feel uncomfortable and constrained, try instead keeping a â€Å"done† list and writing down tasks after you complete them. Brainstorming for competition entries I wrote two or three short stories every month last year, most of them aimed at competitions with a set theme. A notebook is a great place to begin the idea-generation process; I like mind-mapping, by jotting the theme in a central circle and scribbling different plot and character possibilities around the edge. Once you get beyond the first few trite storylines, some intriguing ideas start to emerge. Character sketches When taking part in NaNoWriMo last year, I wrote three or four page character biographies for each of my main characters. Keeping these in my notebook made it easy to find them whilst working on the novel – I wasted as little time as possible when needing to look up details of family backgrounds, hobbies and so on. Plot outlines Most writers find that some level of outlining helps, particularly when writing anything longer than a short story. A notebook can be an easy way to develop a plot from initial spark through potential variations to a scene-by-scene breakdown. Snatches of dialogue Imagined or overheard phrases can be safely stashed in your notebook for future use: they may be totally inappropriate for the project which you’re currently working on, but could be invaluable a week or two down the line. Reviewing your notes It’s just as important to go back over your notes as it is to write them in the first place. Set aside a chunk of time – half-an-hour if possible – weekly, and go over what you’ve written during the past seven days. Make a new entry to record any ideas that you definitely want to pursue. (You might find it helps to use a second notebook at this stage.) Don’t recycle or burn old notebooks; even if you’re sure that you’ll never want the notes contained in them, store them safely somewhere. They’ll make fascinating reading a year, or ten years, further into your writing career – you’ll be able to see how far you’ve come, and you may rediscover old ideas that you’d forgotten. And if you become famous, perhaps you’ll even end up selling them on e-bay†¦ Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Fiction Writing category, check our popular posts, or choose a related post below:20 Great Similes from Literature to Inspire YouLoan, Lend, Loaned, LentParticular vs. Specific