Modeling integers
When modeling integers, we can use colored chips to represent integers. One color can represent a positive number and another color can represent a negative number Here, a yellow chip will represent a positive integer and a red chip will represent a negative integer For example, the modeling for 4, -1, and -3 are shown below: It is extremely important to know how to model a zero. For example, all the followings represent zero pair(s) And so on... Adding and subtracting integers with modeling can be extremely helpful if you are having problems understanding integers In modeling integers, adding and subtracting are always physical actions. If a board is used with the chip, adding always mean " Add something to the board" and subtraction always mean "Remove something from the board" Here, we will use a big square to represent a board Let's start with addition of integers: Example #1: -2 + -1 Put two red chips on the board. Notice that big arrow represents the "+" sign or the action of adding
7.1.6. What are outliers in the data?
The data set of N = 90 ordered observations as shown below is examined for outliers: The computations are as follows: Median = (n+1)/2 largest data point = the average of the 45th and 46th ordered points = (559 + 560)/2 = 559.5 Lower quartile = .25(N+1)th ordered point = 22.75th ordered point = 411 + .75(436-411) = 429.75 Upper quartile = .75(N+1)th ordered point = 68.25th ordered point = 739 +.25(752-739) = 742.25 Interquartile range = 742.25 - 429.75 = 312.5 Lower inner fence = 429.75 - 1.5 (312.5) = -39.0 Upper inner fence = 742.25 + 1.5 (312.5) = 1211.0 Lower outer fence = 429.75 - 3.0 (312.5) = -507.75 Upper outer fence = 742.25 + 3.0 (312.5) = 1679.75 From an examination of the fence points and the data, one point (1441) exceeds the upper inner fence and stands out as a mild outlier; there are no extreme outliers.
Open University
Copyrighted image Credit: The Open University Open2.net fades away... For ten years, give or take, Open2.net was the online home of Open University and BBC programming. Over the last few months, though, we've been moving into OpenLearn, creating one home for all The Open University's free learning content. It means we share a home with the Open University's iTunesU and YouTube channels, and much more besides. You can use the navigation at the top of this page to explore what we have on offer. There's lots to do - you could watch Evan Davis exploring the state of British manufacturing7; explore the frozen planet8; get to know the science and history of the Olympics9 or have a look at our free courses. Most of the content from Open2.net has been brought across; if you've landed here after typing or searching for an Open2.net URL then you're probably looking for something that fitted into one of these categories: Open2 forums We still want you to join in, comment and share your views.
Binary numeral system
The binary or base-two numeral system is a representation for numbers that uses a radix of two. It was first described by Gottfried Leibniz, and is used by most modern computers because of its ease of implementation using digital electronics--early 20th century computers were based the on/off and true/false principles of Boolean algebra. Binary can be considered the most basic practical numeral system (the Unary system is simpler, but impractical for most computation). Representation A binary number can be represented by any set of bits (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states. The following could all be interpreted as binary numbers: 0101001101011 on off off on off on + - - + - + Y N N Y N Y In keeping with customary representation of numerals using decimal digits, binary numbers are commonly written using the symbols 0 and 1. 100101 binary (explicit statement of format) 100101b (a suffix indicating binary format)
How to Read and Use a Box-and-Whisker Plot
The box-and-whisker plot is an exploratory graphic, created by John W. Tukey, used to show the distribution of a dataset (at a glance). Think of the type of data you might use a histogram with, and the box-and-whisker (or box plot, for short) could probably be useful. The box plot, although very useful, seems to get lost in areas outside of Statistics, but I’m not sure why. It could be that people don’t know about it or maybe are clueless on how to interpret it. Reading a Box-and-Whisker Plot Let’s say we ask 2,852 people (and they miraculously all respond) how many hamburgers they’ve consumed in the past week. Take the top 50% of the group (1,426) who ate more hamburgers; they are represented by everything above the median (the white line). Find Skews in the Data The box-and-whisker of course shows you more than just four split groups. Want to learn more about making data graphics?
Sheppard Software: Fun free online learning games and activities for kids.
Excel Box and Whisker Diagrams (Box Plots)
Box and Whisker Charts (Box Plots) are commonly used in the display of statistical analyses. Microsoft Excel does not have a built in Box and Whisker chart type, but you can create your own custom Box and Whisker charts, using stacked bar or column charts and error bars. This tutorial shows how to make box plots, in vertical or horizontal orientations, in all modern versions of Excel. In its simplest form, the box and whisker diagram has a box showing the range from first to third quartiles, and the median divides this large box, the “interquartile range”, into two boxes, for the second and third quartiles. Sample Data and Calculations To play along at home in Excel 2007 or 2010, download the workbook Excel_2007_Box_Plot_Workbook.xlsx. Let’s use the following simple data set for our tutorial. All of these values are positive. First, insert a bunch of blank rows, and set up a range for calculations. First, compute some simple statistics, such as the count, mean, and standard deviation.
Maths and Stats by Email | Why is A4 paper the size that it is? Tangrams
You will need Copy of the printout Scissors Pens or pencils (optional) What to do Cut out each of the pieces. What’s happening? To finish this puzzle you have to take two smaller squares and turn them into one large square. When you finish the puzzle, you’ll find the largest triangles have their diagonals along the edges of the square. Applications If you started out with two squares, each 1 metre across, the resulting large square would have a side length of √2 metres. √2 is an important number – when you multiply √2 by itself, you get 2. √2 is a tricky number to write down. For any square, to find its diagonal, simply multiply the side length by √2. More information Try tangram puzzles online
