Upper quartile

The probabihty-density function for the normal distribution cui ve calculated from Eq. (9-95) by using the values of a, b, and c obtained in Example 10 is also compared with precise values in Table 9-10. In such symmetrical cases the best fit is to be expected when the median or 50 percentile Xm is used in conjunction with the lower quartile or 25 percentile Xl or with the upper quartile or 75 percentile X[j. These statistics are frequently quoted, and determination of values of a, b, and c by using Xm with Xl and with Xu is an indication of the symmetry of the cui ve. When the agreement is reasonable, the mean v ues of o so determined should be used to calculate the corresponding value of a. 

Fig. 8.18. Representation of some trace elements in wines in form of boxplots, constructed as follows box lower quartile, median , and upper quartile whiskers minima and maxima within box 1.5 of the quartiles difference outliers 0 outside of box 1.5 of quartiles difference (according to Danzer et al. [2001])...

Wash Temperature (°C) Upper Quartile Length (mm) Mean Length (mm) Short Fibers (%)... 

Median, minimum, maximum, and upper quartile values are given in Table 1. The 7 sites with pH values below 5.1 are all from ponds in the Pebble West area, concentrated where sulphide-bearing rubble crop is exposed or under thin cover. All but two of the 32 sites with pH values below 5.88 (lower quartile) are from surface and ground water samples in and adjacent to the Pebble deposit. Borehole seeps are all circum-neutral. 

Many surface waters are extremely dilute (low tens of pS/cm). The lowest specific conductance values are from ponds peripheral to or outside the deposit area. Samples with specific conductance above 89 pS/cm (upper quartile) are from ponds and ground waters within or close to the deposit area. The highest values are from borehole seeps that probably reflect a deeper ground water source. 

Copper, Ni, Re, the rare earth elements (REE), and Tl exhibit similar distributions with the upper quartile of data from samples centred about Pebble West. These elements occur in ponds, springs, and borehole seeps, but are highest in the low-pH ponds. Curiously, elevated values of Cu and REE are not present in borehole seeps (circum-neutral pH). 

For pond and spring waters, nearly the entire upper quartiles of both Ag and Mo data fall within a 10-km area centred on the Pebble deposit. 

A second, simple measure of variability is the inter-quartile range that is the interval between the upper and lower quartiles. The upper quartile of a set of data is that value that is less than 25% of the data and greater than 75% similarly, the lower quartile is the value that is greater than 25% of the data and less than 75%. For the blood glucose data the lower quartile is 3.6 mmol / Land the upper quartile 4.55 mmol/L, giving an interquartile range of 0.95 mmol/L. 

This method gives those subjects who withdraw for positive reasons the best possible outcome value for the endpoint and those who withdraw for negative reasons, the worst value. This may seem a little extreme and a lesser position would be to look at the distribution of the endpoint for the completers and to use say the upper quartile (the value that cuts off the best 25 per cent of values) for those subjects withdrawing for positive reasons and the lower quartile (the value that cuts off the worst 25 per cent of values) for those subjects who withdraw for negative reasons. 

Alternative applications of these rules would be to use the best case value (or the upper quartile) for subjects in the control group and the worst case value (or the lower quartile) for subjects in the test treatment group. Certainly if the treatment comparison is preserved under such a harsh scheme then we can be very confident of a true benefit for the test treatment ... 

Eikelboom 488 75-325 5 yr Urinary 11- Elevated urinary 25 Upper quartile had... 

Method No. Bond Distances Mean Median Minimum Maxiumum Range Lower Quartile Upper Quartile Interquartile Range Standard Deviation... 

Identify (or eliminate) outliers by a criterion based on the central 50% of the distribution, thus reducing the masking effect of several outliers. Compute the interquartile range (JQR) between the lower and upper quartiles of the distribution (Qi and Q3, respectively) IQR Q3 - Qi. Then identify as outhers data lying outside the two fences Qi - 1.5 IQR and Q3 +... 

Fig. 3 Box-plot of MTBE concentrations found in the vicinity of an airport (A) at different water bodies and (B) detailed for coastal water samples ( = 8) through seven sampling campaigns. For each variable, the box has lines at the lower quartile (25%), median (50%), and upper quartile (75%) values. The whiskers are the lines extending from each end of the box to show the extent of the data up to 1.5 times the interquartile range (IQR). The mean value is marked with (a) and outliers with (x) symbols. Each sample ( ) was analyzed in triplicate, and the average value was considered for calculations. Non-detected levels were expressed as half of instrumental limit of detection (5 X 10 rgL )...

The statistics chosen for tabulation effectively describe the distribution of bond lengths in each case. For a symmetrical normal distribution the mean (d) will be approximately equal to the median (w) the lower and upper quartiles will be... 

Distribution plot of 421 samples. Data were analyzed in a statistical program and showed the following mean = 13.18 mode = 1 1.68 median = 12.00 lower quartile =10 upper quartile = 16 interquartile range = 6 standard error of mean (SEM) - 0.28 variance = 33.20 SD = 5.76 CV = 0.44. 

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