At least 25% of the values are equal to five. Twenty-five percent of the values are between one and five, inclusive.
In this case, at least 25% of the values are equal to one. For example, if the smallest value and the first quartile were both one, the median and the third quartile were both five, and the largest value was seven, the box plot would look like:
The right side of the box would display both the third quartile and the median. In this case, the diagram would not have a dotted line inside the box displaying the median. For instance, you might have a data set in which the median and the third quartile are the same. The following data are the number of pages in 40 books on a shelf. The middle 50% (middle half) of the data has a range of 5.5 inches.The interval 59–65 has more than 25% of the data so it has more data in it than the interval 66 through 70 which has 25% of the data.But 10.2 is fully below the lower outer fence, so 10.2 would be an extreme value.= 70 - 64.5 = 5.5\). Since 16.4 is right on the upper outer fence, this would be considered to be only an outlier, not an extreme value.
Then the outliers will be the numbers that are between one and two steps from the hinges, and extreme value will be the numbers that are more than two steps from the hinges. The outliers (marked with asterisks or open dots) are between the inner and outer fences, and the extreme values (marked with whichever symbol you didn't use for the outliers) are outside the outer fences.īy the way, your book may refer to the value of " 1.5×IQR " as being a "step". If your assignment is having you consider not only outliers but also "extreme" values, then the values for Q 1 − 1.5×IQR and Q 3 + 1.5×IQR are the "inner" fences and the values for Q 1 − 3×IQR and Q 3 + 3×IQR are the "outer" fences. The values for Q 1 − 1.5×IQR and Q 3 + 1.5×IQR are the "fences" that mark off the so-called reasonable values from the outlier values. Who knows? But whatever their cause, the outliers are those points that don't seem to fit. Maybe you bumped the weigh-scale when you were making that one measurement, or maybe your lab partner is an idiot and you should never have let him touch any of the equipment. That is, if a data point is below Q 1 − 1.5×IQR or above Q 3 + 1.5×IQR, it is viewed as being too far from the central values to be reasonable. An outlier is any value that lies more than one and a half times the length of the box from either end of the box. The IQR is the length of the box in your box-and-whisker plot. How do outliers relate to the Inter-Quartile Range? These "too far away" points are called outliers, because they lie outside the range in which we expect them. The IQR tells how spread out the middle (or the bulk of the) values are it can also be used to tell when some of the other values are, in some sense, "too far" from the central value(s). Statistics assumes that your values are clustered around some central value. They are points way off to one end or the other, which are discarded as being "noise", a mismeasurement, or some other sort of error. Outliers are data points which are regarded as being too far from the bulk of the data points to be valid.
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