Guide :

What is a stem and leaf plot and when would I use one?

I understand bar graphs, and graphing functions, but why would I use a stem and leaf plot?

Research, Knowledge and Information :


Stem and Leaf Plots - Math is Fun - Maths Resources


Stem and Leaf Plots. A Stem and Leaf Plot is a special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last ...
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Stem-and-leaf display - Wikipedia


A stem-and-leaf display is a device for presenting quantitative data in a graphical ... A simple stem plot may refer to plotting a matrix of y values onto a common x ...
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What is the Stem and Leaf Plot? An Overview - ThoughtCo


What does this Stem and Leaf Plot Show? The Stem shows the 'tens' and the leaf. At a glance, one can see that 4 students got a mark in the 90's on their test out of 100.
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Stem-and-Leaf Plots | Purplemath


Explains how to create a stem-and-leaf plot from a data set. ... I'll use the tens digits as the stem values and the ones digits as the leaves.
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Stem-and-Leaf Plots: Examples | Purplemath


Demonstrates some options for stem-and-leaf plots, ... I can plot them all on one stem-and-leaf plot by drawing leaves on either side of the stem I will use the ...
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How to Make a Stem and Leaf Plot - Tutorial - ThoughtCo


See how to make a stem and leaf plot, ... One type of graph that displays these features of the data is called a stem and leaf plot, or stemplot.
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Stem-and-leaf plots (video) | Khan Academy


A statistician for a basketball team tracked the number of points that each of the 12 players on the team had in one game. And then made a stem-and-leaf plot to show ...
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Stem-and-Leaf Plots - McGraw-Hill Education


Objective To use stem-and-leaf plots for organizing and ... plot until only one (or two) ... Ask students to use the stem-and-leaf plot on journal page 10 to
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Stem and Leaf Plot - YouTube


Feb 03, 2009 · 6-6 Stem-and-Leaf Plots and Mean, Median, and Mode - Duration: 13:59. ... Edexcel S1 Tutorial 6 Stem and Leaf Plot and Outliers - Duration: 18:57.

Suggested Questions And Answer :


how do i do stem and leaf plot in math

Look at your numerical data. What is the highest power of ten (units (ones), tens, hundreds, thousands, millions, etc.)? Now you need to make sure that all the numbers in the dataset are standardised to that highest order. That may mean putting in leading zeroes. So if, for example, you had numbers between 0 and 99 then the highest power of ten is the tens order. If you have a number less than 10, put a zero in front of it, so 7 would be 07. The stem is simply the first digit of the data. So in this case you may have stems 0-9 representing the tens place. The remaining digits form the leaf. So in your stem and leaf table you put the stems at the beginning of each row. These start the horizontal lines of the table: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Now put in the leaves filling up cells along the rows. So, for example, 07 would be in the first row, stem 0. It would occupy the next cell on the right of the stem. If you had, for example, 23 and 29 in your dataset, you would go to row stem 2 and put 3 and 9 in adjacent cells. Fill the table with your data just as it comes. The placement of the leaves forms a shape. There are more cells filled for some stem rows and they project further to the right than stems with fewer leaves. This is a frequency plot. Now tidy up the table be arranging the leaf cells into numerical order along the lines starting with the smallest. This makes the plot more useful to draw information from. If the data has a large range, the stems could be, for example, all the numbers between 0 and 49, 50-99, 100-149, etc. The same principle applies. You just put in the whole data for the stems along the stem rows. But usually you will find that the first digit idea is the most common one for stem and leaf plots. Think of the stem and leaf idea as a filing cabinet. Just as you might have all folders for subjects beginning with A in a drawer marked A, folders for B-subjects in a drawer marked B and so on, all in alphabetical order in their own drawers, you can think of each drawer as a stem row. The filing cabinet can be thought of as the stem and leaf plot where the contents of each drawer are the leaves. Some drawers will contain more folders (leaves) than others. If your filing cabinet were made of glass you would be able to see which drawers contained the most folders and which the least. Stem and leaf plots use numerical ordering and this is similar to alphabetical ordering in a filing cabinet or library catalogue.
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What is a stem and leaf plot and when would I use one?

Stem and Leaf plots are just a method of ordering data in a dataset to produce a frequency chart. These plots are used in statistical analysis to draw conclusions about a dataset. The usual way this is done is to use part of each datum to create a data bin. Let's imagine a dataset where all the data consists of numbers between 1 and 99. It doesn't matter how big the dataset is or if there are duplicates. Now imagine 10 bins. The first bin is for numbers between 1 and 9; the second for numbers between 10 and 19, and so on. The numbers of the bins will be labelled 0 to 9. The bins are the stems. So we just go through all the data and put each datum into its appropriate bin. But we don't have to put the whole of the data into each bin, because the bin number is already numbered with the first digit of the data. So the contents of each bin just contain the second digit of the data. The bins (stems) are lined up in order 0 to 9 and we can also stack their contents so that the single digits are in order inside the bins. These are the leaves. Imagine the bins are made of glass. We can look at the bins and the heights of the stacks of contents. The heights of the contents form a shape as we run down the line of bins. These heights tell us how many data there are in each bin and indicate where the most data is and where the least data is. This is is a frequency distribution. It's the basis of the Stem and Leaf plot and can be represented by a table or chart. Each row of the table starts with the bin number (STEM) and along the row we have the contents of the bin (LEAVES). Turn the table on its side and we have a chart with the stem running along the bottom and the leaves forming towers over the stems. The chart resembles the row of bins with the stack, or column, of contents over them, but the bins are now invisible, and only their labels remain as regular horizontal divisions on the chart. But it doesn't stop there. This frequency chart tells us where most of the data can be found, where its middle is and the general shape of the data. These are important statistical observations. Not all the bins may have data in them, and some will have lots of data. Random data will produce no particular shape, but in many cases there will be a pattern. We've considered numbers from 1 to 99, but the data can have any range as long as the data is binned carefully to reflect the relative magnitude of the data. If the data were between 250 and 400, for example, we might take the first 2 digits as the bin label: 25 to 40 and the contents would be the third digit. So you need to make a decision based on the range of data values to decide how the data is going to be binned. I hope this helps you to understand Stem and Leaf plots.
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How do I read Stem and Leaf plots?

Stem and Leaf plots are just a method of ordering data in a dataset to produce a frequency chart. The usual way this is done is to use part of each datum to create a data bin. Let's imagine a dataset where all the data consists of numbers between 1 and 99. It doesn't matter how big the dataset is or if there are duplicates. Now imagine 10 bins. The first bin is for numbers between 1 and 9; the second for numbers between 10 and 19, and so on. The numbers of the bins will be labelled 0 to 9. The bins are the stems. So we just go through all the data and put each datum into its appropriate bin. But we don't have to put the whole of the data into each bin, because the bin number is already numbered with the first digit of the data. So the contents of each bin just contain the second digit of the data. The bins (stems) are lined up in order 0 to 9 and we can also stack their contents so that the single digits are in order inside the bins. These are the leaves. Imagine the bins are made of glass. We can look at the bins and the heights of the stacks of contents. The heights of the contents form a shape as we run down the line of bins. These heights tell us how many data there are in each bin and indicate where the most data is and where the least data is. This is is a frequency distribution. It's the basis of the Stem and Leaf plot and can be represented by a table or chart. Each row of the table starts with the bin number (STEM) and along the row we have the contents of the bin (LEAVES). Turn the table on its side and we have a chart with the stem running along the bottom and the leaves forming towers over the stems. The chart resembles the row of bins with the stack, or column, of contents over them, but the bins are now invisible, and only their labels remain as regular horizontal divisions on the chart. But it doesn't stop there. This frequency chart tells us where most of the data can be found, where its middle is and the general shape of the data. These are important statistical observations. Not all the bins may have data in them, and some will have lots of data. Random data will produce no particular shape, but in many cases there will be a pattern. We've considered numbers from 1 to 99, but the data can have any range as long as the data is binned carefully to reflect the relative magnitude of the data. If the data were between 250 and 400, for example, we might take the first 2 digits as the bin label: 25 to 40 and the contents would be the third digit. So you need to make a decision based on the range of data values to decide how the data is going to be binned. I hope this helps you to understand Stem and Leaf plots.
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when building a stem and leaf plot, do you include the stem if there is no leaf

If the stem is in the range for the whole plot, then, yes, you would include it. If it is outside the range then there's no point in including it. If, for example, all the data was in the range 200 to 849 then you could have a stem based on the first 2 digits of the data: 20 to 84. If there were no data between 500 and 600 you would still include 50 as a stem so that you get a proper picture of the data organisation in the range. But there would be no point in including 10 or 90 as stems because there are no leaves for these stems. 
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How to plot

I guess you want to use Excel to plot a binomial distribution where the probability is p=0.25. Excel will plot a graph for non-cumulative and cumulative distribution. You use the BINOMDIST statistical function, which has 4 parameters:   number of successes (x axis); total number of trials, n; the probability, p; whether cumulative or not. You set these up in a table for Excel to use to do the plots, with a fixed cell for the probability and columns for the number of successes and the corresponding values to contain the results of applying BINOMDIST.  The question asks for three graphs, so what could they be? The BINOMDIST function has 4 parameters, and the question supplies only one. So we can use Excel to plot graphs where the other parameters are different. We can change the number of trials; we can choose whether cumulative or non-cumulative; we can change the range of successes. So we set up three tables. The first table has fixed cells for n, p and cumulative=FALSE, and values in a column from 0 to n for the number of successes to be plotted; second table has the same but cumulative=TRUE; the third has a different n and successes column and cumulative can be either TRUE or FALSE. You would specify the continuous curve type of graph for Excel to plot the data as a curve and the result would show the typical bell-shaped binomial distribution curve for the non-cumulative distribution and the hill-shaped curve for the cumulative. To use the graphs, you read off for each x value (number of successes required) the percentage or fraction of the expected results. You would also title the graph, label its axes and show that p=0.25 is the active probability. Excel will allow you to customise how you want the graphs to look. [Non-cumulative means the exact number of successes expected in a given number of trials; cumulative means at least or at most the specified number of successes in a given number of trials.]
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explain complex number and vectors

Start with real numbers. A number line is often used to represent all real numbers. It has infinite length and somewhere we can mark zero, dividing positive numbers (on the right of zero) and negative numbers (on the left of zero). The line is continuous so no real number can be left out. A line is 1-dimensional. A complex number has two components: one real, the other imaginary. A complex number can be represented by a plane, and it's 2-dimensional. So what does imaginary mean? The basis of imaginary numbers is the square root of minus one (sqrt(-1)) and traditionally it is given the symbol i. The square root of any negative number can be expressed using i. So, for example, the square root of minus 4 is 2i, because -4=4*-1 and the square root of 4*-1 is 2sqrt(-1)=2i. A complex number, z, can be written a+ib, where a and b are real numbers. But, more importantly perhaps, they can be represented as a point in 2-dimensional space as the point (a,b) plotted on a graph using the familiar x-y coordinate system. So, just like the number line represented all real numbers like an x axis, so all complex numbers can be represented by a plane, an infinite x-y plane. Now we come to vectors. There is a commonality between complex numbers and vectors. A straight road with cars , houses, people, etc., on it make the road like a number line. Any position on the road can be related to a fixed point on the road we'll call "home". Objects to the right, or eastward, could be in front of home and those to the left, or westward, behind home. The position of an object is the distance from home. This is a 1-dimensional vector field, where all objects have position. If the objects move their speed will have direction, towards the right or towards the left and we can say that a speed to the right is positive and a speed to the left is negative. Now we introduce another straight road at right angles to the first road. Now the picture is 2-dimensional. The position of an object is defined by two values: position east or west and position north or south. North can be positive and south negative. This is equivalent to the complex plane, which represents all complex numbers. The 2-dimensional plane represents all 2-dimensional vectors, whether it's position or speed. But the word "velocity" is used instead of "speed", because velocity includes direction, but speed is just a number, or magnitude, of the velocity. A vector has an east-west (EW) component (x value) and a north-south (NS) component (y value) and a vector r=xi+yj, where i is called a unit vector in the NS direction and j in the EW direction, so the point (x,y) fixes the positional vector r. Vectors are usually written in bold type, so you won't confuse i with i. The magnitude of a vector is sqrt(x^2+y^2) so it is represented by the hypotenuse of a right-angled triangle whose other sides are x and y. Pythagoras' theorem is used to work out the value. The magnitude of a vector is sometimes written |r| and is called a "scalar" quantity, so it doesn't have a direction or a sign (positive or negative), because the sign is a property of the direction of the vector.  A vector is not limited to a 2-dimensional plane. It can have as many dimensions as necessary. An aeroplane's positional vector and velocity would involve another dimension: height. A submarine's positional vector and velocity would involve depth. Height and depth are perpendicular to the EWNS plane and together form 3-dimensional space. The unit vector for height and depth is k, and height would be positive while depth would be negative, and the letter z is used with x and y so that a point in 3-space is (x, y, z). The magnitude |r| is sqrt(x^2+y^2+z^2). When working with vectors, addition and subtraction requires adding and subtracting the x, y, z components separately. When adding or subtracting complex numbers, the same applies to the x and y, real and complex, components. Multiplication and division are a special topic beyond the scope of this introductory explanation.  
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What's a function of function?

If you just mean the purpose of a function then see immediately below. If you mean f of g where f and g are two functions, go to the end. The purpose of a function is like giving someone a to-do list. A function (normally shown as f(x)= meaning "function of x", or y=) will usually contain one variable, usually represented by x. Some functions may have more than one variable. If x isn't the variable, it will usually be a different letter like t or a or any letter. Let's say it is x. This variable will appear in a formula with numbers. The formula is the function and it contains instructions in symbols telling you what to do with the variable. For example, multiply the variable by 2 then add 3 and divide the result by 4. This would be written f(x)=(2x+3)/4 or y=(2x+3)/4. The equals sign means that the function is defined as the expression on the right. Just like someone might say to you, think of a number (that's x), but don't tell me what it is, then double it and add 3 and divide the result by 4. Functions can be plotted on a graph. The idea of this is that on the horizontal axis (x axis) you have markers for 0, 1, 2, etc. On the vertical axis (y or f(x)) you also have markers. The graph is usually a continuous line, and every point on the line is made by putting a different value for x and marking the point (on a rectangular grid f(x) units vertically and x units horizontally) for the result of working out the value of the function for different values of x. The points make up the graph. You can use the graph to find the value of x for any value of the function, and the value of the function for any value of x, provided the graph extends far enough. This is just a brief example of the purpose of a function. A practical example is the conversion of temperature in degrees Fahrenheit (F) to degrees Celsius: C=5(F-32)/9. This function tells you what do with the value of the temperature. You could plot this as a straight line graph and you can read off degrees C for any temperature in degrees F, and vice versa. Another example is d=30t where d=distance, speed=30mph, t=time. The function is 30t, and from it you can work out the distance a car moves in a particular time t when its speed is 30mph. Function of a function: this simply means you work out the value of applying one function and then feed this answer as the variable into the other function. An example could be that one function is used to find out how many miles a car travelling at an average speed of 30mph in a given time. The second function could be to find out how much fuel is used to travel that distance. So g(t)=30t is the first function. The second function is h(d)=d/24 where fuel consumption is 24 miles per gallon. h of g is h(g(t))=30t/24=5t/4.
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7x+2y=5 and 3y=16-2x

7x+2y=5 and 3y=16-2x  solve each of the following systems using the method of youre choice. However, you must show an organize work. We could solve both equations, but what would we have? We would still have two equations. Each would show y in terms of x, or x in terms of y. We still wouldn't know the values of x or y. E.g., y = 16/3 - 2/3 x (the second equation) When you are given two equations in the same problem, you can be sure that you are supposed to solve them simultaneously, to find the one unique pair of x,y values that will solve both equations. Let's proceed with that thought in mind. 7x+2y=5   3y=16-2x -> rewrite the second:  2x + 3y = 16 We'll eliminate the y terms by subtracting one equation from the other. To do that, the y terms must be the same. 3 * (7x+2y) = 3 * 5           21x + 6y = 15 2 * (2x + 3y) = 2 * 16      (  4x + 6y = 32)                                     ----------------------- Subtract and get---->       17x         = -17 17x = -17 x = -1 We will substitute that x value into the first equation. 7*(-1) +2y = 5 -7 + 2y = 5 2y = 12 y = 6 Finally, substitute both values, x and y, into the second equation. 3 * 6 = 16 - (2 * -1) 18 = 16 - (-2) 18 = 18 Now, you know that x=-1 and y=6 solves both equations at the same time. This tells you that if you plot the two equations on the same graph, you will have two lines that intersect at (-1, 6).  
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STEM AND LEAF PLOT TO SHOW DATA.

STEM AND LEAF PLOT (FREQUENCY DISTRIBUTION) STEM (tens of dollars)   L E A F   ( u n i t s )   0 6 9 9                       1 1 2 2 2 3 3 4 5 5 5 5 7 7 8 2 0 0 5                        
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a data display that plots ones digits as a leaf from the tens digets

The tens digit is the stem in a Stem and Leaf plot.
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