Statistics for me ….

Both Quoted from Wikipedia

In descriptive statistics, the interquartile range (IQR), also called the midspread or middle fifty, is a measure of statistical dispersion, being equal to the difference between the third and first quartiles.

Unlike the (total) range, the interquartile range is a robust statistic, having a breakdown point of 25%, and is thus often preferred to the total range.

The IQR is used to build box plots, simple graphical representations of a probability distribution.

For a symmetric distribution (so the median equals the midhinge, the average of the first and third quartiles), half the IQR equals the median absolute deviation (MAD).

The median is the corresponding measure of central tendency.IQR = Q3 − Q1

In descriptive statistics, a box plot or boxplot (also known as a box-and-whisker diagram or plot) is a convenient way of graphically depicting groups of numerical data through their five-number summaries: the smallest observation (sample minimum), lower quartile (Q1), median (Q2), upper quartile (Q3), and largest observation (sample maximum). A boxplot may also indicate which observations, if any, might be considered outliers.

Boxplots display differences between populations without making any assumptions of the underlying statistical distribution: they are non-parametric. The spacings between the different parts of the box help indicate the degree of dispersion (spread) and skewness in the data, and identify outliers. Boxplots can be drawn either horizontally or vertically.

How to read a box plot: from (

In statistical analysis, a box plot is a graph that can be a valuable source of easy-to-interpret information about a sample of study. A box plot can provide information about a sample’s range, median, normality of the distribution, and skew of the distribution. It can also identify and plot extreme cases within the sample.

Box and Whiskers:

The box plot shows a box encased by two outer lines known as whiskers. The box represents the middle 50% of the data sample – half of all cases are contained within it. The remaining 50% of the sample is contained within the areas between the box and the whiskers, with some exceptions (these exceptions are called outliers and they will be discussed more extensively later). For example, consider a sample of 100 IQ scores. The bottom 25% of the scores would be represented by the space between the lower whisker and the box, the middle 50% would be within the box, and the remaining 25% would be contained between the box and the upper whisker.

Box Position:

The location of the box within the whiskers can provide insight on the normality of the sample’s distribution. When the box is not centered between the whiskers, the sample may be positively or negatively skewed. If the box is shifted significantly to the low end, it is positively skewed; if the box is shifted significantly to the high end, it is negatively skewed.

Box Size:

The size of the box can provide an estimate of the kurtosis – the peakedness – of the distribution. A very thin box relative to the whiskers indicates that a very high number of cases are contained within a very small segment of the sample. This signifies a distribution with a thinner peak. A wider box relative to the whiskers indicates a wider peak. The wider the box, the more U-shaped the distribution becomes.


Outliers are not present in every box plot. When they are present, they are found in the form of points, circles, or asterisks outside of the boundaries of the whiskers. These are extreme values that deviate significantly from the rest of the sample and they can exist above or below the whiskers of the box plot.

What I’ve got today …a boxplot from 1 of the experiment…its easy to draw this using matlab – simply by boxplot([a,b,c,d,e,f,g,h,i,j,k])