# Iqr and standard deviation relationship

### The idea of spread and standard deviation (article) | Khan Academy

What are some uses of interquartile range and standard deviation? Their relation is much like that between the mean and the median - the. Grading on a curve in college instilled a habit for using mean and standard deviation to describe a set of continuous data points. On any given. Standard deviation measures the spread of a data distribution. The more spread out a . standard deviation · Comparing range and interquartile range (IQR).

Like mean and standard deviation, median and IQR measure the central tendency and spread, respectively, but are robust against outliers and non-normal data. They have a couple of additional advantages: IQR makes it easy to do an initial estimate of outliers by looking at values more than one-and-a-half times the IQR distance below the first quartile or above the third quartile.

Comparing the median to the quartile values shows whether data is skewed. For example, Group I has a high proportion of larger values, and the median is therefore closer to the third quartile than the first quartile. By contrast, the values in Group II are more evenly distributed. Excel has built-in functions for all of these, except outliers, which can be computed using a basic formula.

For example, the examination marks for 20 students following a particular module are arranged in order of magnitude. Like the range however, the inter-quartile range is a measure of dispersion that is based upon only two values from the dataset. Statistically, the standard deviation is a more powerful measure of dispersion because it takes into account every value in the dataset.

The standard deviation is explored in the next section of this guide. Calculating the Inter-quartile range using Excel The method Excel uses to calculate quartiles is not commonly used and tends to produce unusual results particularly when the dataset contains only a few values. For this reason you may be best to calculate the inter-quartile range by hand. The Standard Deviation The standard deviation is a measure that summarises the amount by which every value within a dataset varies from the mean.

Effectively it indicates how tightly the values in the dataset are bunched around the mean value. It is the most robust and widely used measure of dispersion since, unlike the range and inter-quartile range, it takes into account every variable in the dataset. When the values in a dataset are pretty tightly bunched together the standard deviation is small. When the values are spread apart the standard deviation will be relatively large.

### Mean and standard deviation versus median and IQR (video) | Khan Academy

The standard deviation is usually presented in conjunction with the mean and is measured in the same units. In many datasets the values deviate from the mean value due to chance and such datasets are said to display a normal distribution. In a dataset with a normal distribution most of the values are clustered around the mean while relatively few values tend to be extremely high or extremely low.

Many natural phenomena display a normal distribution. For datasets that have a normal distribution the standard deviation can be used to determine the proportion of values that lie within a particular range of the mean value. Figure 3 shows this concept in diagrammatical form.

## Australian Bureau of Statistics

If the mean of a dataset is 25 and its standard deviation is 1. If the dataset had the same mean of 25 but a larger standard deviation for example, 2. The frequency distribution for a dispersed dataset would still show a normal distribution but when plotted on a graph the shape of the curve will be flatter as in figure 4.

Population and sample standard deviations There are two different calculations for the Standard Deviation.

Which formula you use depends upon whether the values in your dataset represent an entire population or whether they form a sample of a larger population. For example, if all student users of the library were asked how many books they had borrowed in the past month then the entire population has been studied since all the students have been asked.

In such cases the population standard deviation should be used. Sometimes it is not possible to find information about an entire population and it might be more realistic to ask a sample of students about their library borrowing and use these results to estimate library borrowing habits for the entire population of students.

They're measured in thousands.

## The idea of spread and standard deviation

So one makes 35, 50, 50, 50, 56, two make 60, one makes 75, and one makesSo she's doing very well for herself, and the computer it spits out a bunch of parameters based on this data here. So it spits out two typical measures of central tendency.

The mean is roughly The computer would calculate it by adding up all of these numbers, these nine numbers, and then dividing by nine, and the median is 56, and median is quite easy to calculate.

You just order the numbers and you take the middle number here which is Now what I want you to do is pause this video and think about for this data set, for this population of salaries, which measure, which measure of central tendency is a better measure?

### Statistical Language - Measures of Spread

All right, so let's think about this a little bit. I'm gonna plot it on a line here. I'm gonna plot my data so we get a better sense and we just don't see them, so we just don't see things as numbers, but we see where those numbers sit relative to each other.

So let's say this is zero. Let's say this is, let's see, one, two, three, four, five. So this would bethis is 50,, and let's see. Let's say if this is 50 than this would be roughly 40 right here, and I just wanna get rough. So this would be about 60, 70, 80, 90, close enough. I'm, I could draw this a little bit neater, but, 60, 70, 80, Actually, let me just clean this up a little bit more too. This one right over here would be a little bit closer to this one.

Let me just put it right around here.