![]() The mean of this new data set is about ?252?, and the median of the new data set is ?2.5?. Let’s add a huge value to the data set, like ?1,000?, so that the new data set is ?1,\ 2,\ 3,\ 1,000?. Let’s take an easy example, and use the data set ?1,\ 2,\ 3?. It’s also important that we realize that adding or removing an extreme value from the data set will affect the mean more than the median. Depending on the value, the median might change, or it might not. ![]() The same will be true for adding in a new value to the data set. If we add or remove a data point from the set, it can effect the median, but it may not. If take away a data point that’s above the mean, or add a data point that’s below the mean, the mean will decrease. If we add a data point that’s above the mean, or take away a data point that’s below the mean, then the mean will increase. In fact, adding a data point to the set, or taking one away, can effect the mean, median, and mode. Thinking back to our discussion about the mean as a balancing point, we want to realize that adding another data point to the data set will naturally effect that balancing point. So to summarize, if we multiply our data set by a constant value or divide our data set by a constant value, then the mean, median, mode, range, and IQR will all be scaled by the same amount.Īdding or removing a data point from the set Mean The same will be true if we divide every data point in the set by a constant value: the mean, median, mode, range, and IQR will all be divided by the same value. No matter what value we multiply by the data set, the mean, median, mode, range, and IQR will all be multiplied by the same value. The mean, median, mode, range, and IQR are all doubled when we double the values in the data set.Īnd this will always be true. What we see is that multiplying the entire data set by ?2? multiplies all five measures by ?2? as well. The new measures of central tendency and spread are Again starting with the set ?3,\ 3,\ 7,\ 9,\ 13?, the measures are Let’s look at what happens when we multiply our data set by a constant value. So to summarize, whether we add a constant to each data point or subtract a constant from each data point, the mean, median, and mode will change by the same amount, but the range and IQR will stay the same. The same will be true if we subtract an amount from every data point in the set: the mean, median, and mode will shift to the left but the range and IQR will stay the same. No matter what value we add to the set, the mean, median, and mode will shift by that amount but the range and the IQR will remain the same. What we see is that adding ?6? to the entire data set also adds ?6? to the mean, median, and mode, but that the range and IQR stay the same.Īnd this will always be true. And our new measures of central tendency and spread are If we add ?6? to each data point in the set, the new set is ?9,\ 9,\ 13,\ 15,\ 19?. ![]() What happens to measures of central tendency and spread when we add a constant value to every value in the data set? To answer this question, let’s pretend we have the data set ?3,\ 3,\ 7,\ 9,\ 13?, and let’s calculate our measures for the set. For this $f$, the range is the set of non-negative real numbers while the codomain is the set of all real numbers.Changing the entire data set Shifting (addition and subtraction) Since $f(x)$ will always be non-negative, the number $-3$ is in the codomain of $f$, but it is not in the range, as there is no input of $x$ for which $f(x)=-3$. It is possible there are objects in the codomain for which there are no inputs for which the function will output that object.įor example, we could define a function $f: \R \to \R$ as $f(x)=x^2$. All we know is that the range must be a subset of the codomain, so the range must be a subset (possibly the whole set) of the real numbers. But, without knowing what the function $f$ is, we cannot determine what its outputs are so we cannot what its range is. From this notation, we know that the set of all inputs (the domain) of $f$ isi the set of all real numbers and the set of all possible inputs (the codomain) is also the set of all real numbers. In the function machine metaphor, the range is the set of objects that actually come out of the machine when you feed it all the inputs.įor example, when we use the function notation $f: \R \to \R$, we mean that $f$ is a function from the real numbers to the real numbers. The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |