Two of our most-viewed posts deal with Mode and Median of Grouped Data: how to calculate these statistics for data that is supplied in the form of frequencies for classes of data (bins), rather than the individual data values. Here we’ll complete that topic with a look at the less troublesome cases of Mean and …
We have looked at how to calculate, apply, and undo a percent increase or decrease. Here we will look at some special terms used in business for percent increases, which have been a source of many questions over the years. Finding the markup or margin Markup and margin refer to the profit (difference between cost …
Having discussed how to calculate the percent change between two numbers, and how to apply such a change to one number to get a new number, we need to look at what may be one of the most common types of questions we get: reversing a percent change (increase or decrease) to find the original …
A question we got in March asked about working with percent increases. As I replied to this rather common topic, referring to an archived answer, I was reminded that this would is a very common type of question, and would be a good topic to cover in the blog. So that will be the topic …
We’ve been collecting techniques for finding areas of polygons, mostly using their side lengths. We started with triangles (Heron’s formula), then quadrilaterals (Bretschneider’s formula and Brahmagupta’s formula), and the fact that the largest possible area is attained when the vertices lie on a circle. We’ll look at one more way to find area, using coordinates …
Last time we looked at applying Heron’s formula to problems about the area of a triangle, where knowing the side lengths is enough to determine the area; there was a passing mention of the fact that more is needed for quadrilaterals. We’ll start here with a repeat of that idea, and then look at several …
Last time we looked at a very useful formula for finding the area of any triangle, given only the lengths of its sides. Today I want to look at several problems in which the formula has been used, some of them surprising. Area of a plot of land We’ll start with a straightforward application in …
There is a beautiful formula for the area of a triangle, which many students unfortunately never get to see. In this post we’ll look at that formula and three ways to prove it; next time, I’ll show some examples of how useful it can be. (By the way, you’ll also see it called “Hero’s Formula”, …
(An archive question of the week) Last time we looked at a formula for approximating the mode of grouped data, which works well for normal distributions, though I have never seen an actual proof, or a statement of conditions under which it is appropriate. We have also received questions about a much more well-known, and …
The mode of a list of data values is simply the most common value (or values … if any). When data is grouped (binned) as in a histogram, we normally talk only about the modal class (the class, or group, with the greatest frequency), because we don’t know the individual values. But some sources teach …