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... 

Table 1 Summary of projections from the 21 models included in the MultiModd Data set, for the Mediterranean region (30°N, 10°W-48°N, 40-E) and the AIB emission scenario. Temperature differences (°C) between 2080-2099 and 1980-1999. The table shows the minimum, maximum, median (50%), and 25 and 75% quartile values. The frequency of extremely warm, averaged over the models, is also shown. From Christensen et al. [4]...

Ho et al., 2001 Chinese premenopause n= 132 Estimated isoflavone intake range 7.4-48.3 mg/d. Higher BMD of liunbar spine in the 4 quartile... 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

Box plots, also known as box and whisker plots, are commonly used to display univariate statistics for a given variable across another variable. The statistics typically displayed in a box plot are the minimum, first quartile, median, third quartile, and maximum values. Mean values are often included in box plots as well. The following is a sample box plot of a clinical response measure showing how three different drug therapies compare to one another. 

The results also showed that the age-related increase in serum creatinine was earlier and faster and more linear among subjects in the highest quartile than among those in the lowest quartile. Based on the results, Kim et al. (1996a) concluded that low-level exposure to lead may impair renal function in middle-aged and older men however, the biological significance of a 0.08 mg/dL increase in serum creatinine is unknown. 

Emory et al. (1999) evaluated 103 African-American newborns with the NBAS. Maternal PbB levels were obtained at 6-7 months of pregnancy. No significant differences were found between quartiles across Brazelton Cluster scores. The researchers then compared the low quartile group (maternal PbB 1 pg/dL mean=0.855 pg/dL n=26) with the high quartile group (maternal PbB 2.5 pg/dL mean=4.01 pg/dL n=14) and found modest detrimental effects as determined by four Brazelton item... 

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])...

Figure 6.15 Chart in which the Reference Center (RC) and participant (PART) data sets are compared. This chart shows HER2/Chl7 ratio results from Runs 4-6 of the UK NEQAS ICC and ISH assessments. The heavy bar indicates the median, the limits of the shaded box the inter-quartiles, and the extending lines the minimum and maximum for the range.

Semiquartile Distance. When all the data in a group are ranked, a quartile of the data contains one ordered quarter of the values. Typically, we are most interested in the borders of the middle two quartiles Qx and Q3, which together represent the semiquartile distance and which contain the median as their center. Given that there are N values in an ordered group of data, the upper limit of the jih quartile ( >-) may be computed as being equal to the [(jN — l)/4th] value. Once we have used this formula to calculate the upper limits of Qx and Q3, we can then compute the semiquartile distance (which is also called the quartile deviation, and as such is abbreviated as QD) with the formula QD = (Q3 — Q )/2. 

Quartiles divide the data distribution into four parts corresponding to the 25%, 50%, and 75% percentiles, also called the first (Qi), second (Qt), and third quartile (g3). The second quartile (50% percentile) is equivalent to the median. The interquartile range IQR = Q3 - Qi is the difference between third and first quartile. 

The range of the data is defined as the difference between the maximum and minimum value it is very sensitive to outliers which coincide with either the maximum or minimum or both. The robust counterpart of the range is the inter QUARTILE RANGE (IQR, X iqr). 

IQR is the difference between the third and the first quartile, and thus is not influenced by up to 25% of the lowest and 25% of the largest data. In the case of a normal distribution the theoretical standard deviation cr can be estimated from IQR by... 

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