Lower 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. 

Quartile If a set of observations are ranked in order of magnitude, then the quartiles are those three values which divide the observations into four equal parts, i.e., the lower quartile is that... 

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])...

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. 

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 ... 

FIGURE 6 Summary of measurements of in situ rates of bacterial DOC consumption, calculated as the sum of bacterial production and respiration, and in vitro rates of DOC consumption, calculated from declines in DOC during batch incubations. Box-and-whisker plots show median, and upper/lower quartiles (box), and the range of values (bars). Extreme outliers are denoted by open circles. The in situ consumption rates are from the global dataset of simultaneous measurements of bacterial production and respiration collected by del Giorgio and Cole (1998), with the addition of unpublished data (see text). Because the in situ rates have been measured under a range of temperature, for this comparison the bioassay rates have not been corrected for temperature. 

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

The inter-quartile range as an indicator of dispersion The inter-quartile range is defined as the difference between the upper and lower quartiles (Q3 — Ql). So, for steroid 1 ... 

Figure 6 Relationship between median, upper, and lower quartiles of Al, As, Be, Cd, Cu, Mn, Pb, and Zn, and pH in Czech Republic brooks in the late 1980s. Values were calculated after sorting the water samples n = 12,988) into groups with 0.2 pH unit ranges. Volume-weighted average concentrations in bulk precipitation (o) and throughfall ( ) in 1991 samples from the Bohemian Forest are shown (after Vesely and Majer, 1996, 1998). The declines of Be, Cd, Mn, and Zn at very low pH are likely caused by depletion of exchangeable trace metals from the watershed soils.

With ordinal and quantitative data, the upper and lower quartiles show the range of values within which the middle 50% of individual values fall. This is known as the interquartile range and is the recommended way of describing variability if the median is being used to indicate central tendency. 

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 )...

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. 

Looking from a different perspective, the median represents that point that divides the total frequency into two halves, that is, 50% of the data are found above and below the median, respectively. This point is also termed the middle quartile Q(0.5) or Q2. The quartiles and Qj are then called the lower and upper quartiles, respectively. The lower quartile contains 25% of all measurements. 

The lower adjacent value is obtained from the lower quartile minus the 1.5 times the interquartile range ... 

Indicator Unit Upper quartile Lower quartile... 

This assessment is confirmed by an analysis of successful and less successful organic farms in Germany. Ordering farms by profit per family work unit and comparing farms of the upper and lower quartile respectively (Table 3) reveals that ... 

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