Questions Eliciting Thinking Can you reread the first sentence of the second problem? A difference is described between two values. What are these two values?

One can graphically represent a univariate series by putting the data on an axis. We can add some noise to that the points do not end up on top of one another. Actually, it is just a scatter plot with an added dimension. The "rug" function adds a scatter plot along an axis.

In the following examples, we present the cumulative distribution plot of several distributions.

Check the vocabulary I have used: Box-and-whiskers plot A box-and-whiskers plot is a graphical representation of the 5 quartiles minimum, first quartile, median, third quartile, maximum. This is one of the main uses of this kind of plot: This graphical representation of the quartiles is simpler and more directly understandable than the following, in terms of area.

In this example, there are no outliers. Median Mean 3rd Qu. Their presence may be perfectly normal but you must beware that they might bias later computations -- unless you choose robust algorithms ; they may be due to errors, that are to be corrected; they may also reveal that the distribution is not gaussian and naturally contains many outliers "fat tails" -- more about this later, when we mention the "extreme distributions" and high-frequency intra-day financial data.

Actually, the larger the sample, the more outliers. You can ask R to plot a confidence interval on the median: First, the width of the classes can play a role. But their position, as well, can completely change the histogram and have it look sometimes symetric, sometimes not.

For instance, in neither of the following histograms does the peak look symetric but the asymetry is not in the same direction. If you see the data as a sum of Dirac masses, you can obtain such a function by convolving this sum with a well-chosen "kernel", e.

This density estimation can be adaptive: For instance, a scatterplot, or a gaussian density to compare with the estimated density. The following plot simply sorts the data and tries to pair the first with the last, the second with the second from the end, etc.

The following is a plot of the distance to the median of the n-i -th point versus that of the i-th point. Here, with a points this is a lotwe are still far away from a line.

It might be because of that that this plot it is rarely used One other thing we like, about our data, is when they follow a gaussian distribution -- or any well-known, reference distribution.

In some cases, it is obvious that the distribution is not gaussian: In other cases, it is not that obvious. A first means of checking this is to compare the estimated density with a gaussian density. There is already a function to do that.

The "qqline" function plots a line through the first and third quartiles. In this example, the data are roughly gaussian, but we can see that they are discrete.

Two distributions shifted to the left. If the distribution is more concentrated to the left than the gaussian distribution, the left part of the plot is above the line examples 1, 2 and 4 above. If the distribution is less concentrated to the left than the gaussian distribution, the left part of the plot is under the line example 3 above.

If the distribution is more concentrated to the right than the gaussian distribution, the right part of the plot is under the line examples 3 and 4 above. If the distribution is less concentrated to the right than the gaussian distribution, the right part of the plot is above the line examples 1 and 2 above.

For instance, example 5 can be interpreted as: If the distribution is "off-centered to the left" think: If the distribution is "off-centered to the right" think: If the distribution is symetric think: People sometimes use a quantile-quantile plot to compare a positive variable with a half-gaussian -- it may help you spot outliers:The absolute value of a value or expression describes its distance from 0, but it strips out information on the sign of the number or the direction of the distance.

Absolute value is always positive or zero, and a positive absolute value could result from either a positive or a negative original value.

Absolute value inequalities word problem (video) | Khan Academy |
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Draw the line How to plot a nice graph with sweaty shaky hands I have to make a terrible confession. | |

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When you take the absolute value of a number, the result is always positive, even if the number itself is negative. |

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so the appropriate equation would be a(x-1)-4 right? and i have another question does this apply to any if given graph and asked to find the equation if it is greatest equation graph?

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students who were then studying in UK. Aug 21, · Help me write this absolute value equation as a piecewise equation please? ok. write this as a piecewise equation: y= abs (2x - 4) grupobittia.com the heck is a piecewise equation? Follow. 5 Sometimes functions can only be represented as piecewise, since they do not fit any specific mathematical models for the entire set of Status: Resolved.

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