= (38 + 52 + 58 + … + 166) ÷ 22 = 1854 ÷ 22 = 84.2. That is, 8.42%
Which is larger, the median or the **mean**? Is this what you would have expected based on the
The **mean** is larger. Yes, we would have expected this since the distribution is right
Find the **range** of the data. Make sure to give a single number for your answer.

17 Measures of Central Tendency
17.1 **Mean**, Median, Mode and **Range**
In Units 15 and 16, you were looking at ways of collecting and representing data. In this unit, you will go one step further and find out how to calculate statistical quantities which summarise the important characteristics of the data.

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A generalization of Laplace distribution with location parameter , , and scale parameter
0, is defined by introducing a third parameter 0 as a shape parameter. One tractable class of this generalization arises when is chosen such that 1/ is a positive integer. In this article, we derive explicit forms for the moments of order statistics, and the **mean** values of the **range**, quasi-ranges, and spacings of a random sample corresponded to any member of this class. For values of the shape parameter

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In meta-analysis of continuous outcomes, the sample size, **mean**, and standard deviation are required from included studies. This, however, can be difficult because results from different studies are often presented in dif- ferent and non-consistent forms. Specifically in medi- cal research, instead of reporting the sample **mean** and standard deviation of the trials, some trial studies only report the median, the minimum and maximum val- ues, and/or the first and third quartiles. Therefore, we need to estimate the sample **mean** and standard devia- tion from these quantities so that we can pool results in a consistent format. Hozo et al. [3] were the first to address this estimation problem. They proposed a simple method for estimating the sample **mean** and the sample variance (or equivalently the sample standard deviation) from the median, **range**, and the size of the sample. Their method is now widely accepted in the literature of sys- tematic reviews and meta-analysis. For instance, a search of Google Scholar on November 12, 2014 showed that the article of Hozo et al.’s method has been cited 722 times where 426 citations are made recently in 2013 and 2014.

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Abstract. The forward-backward correlation strength between event-**mean** transverse momenta of particles produced in separated rapidity intervals in high energy hadronic collisions is analyzed in the simple model with the string fusion on a transverse lattice.
The coeﬃcient of long-**range** rapidity p t - p t correlation is obtained using the negative bi- nomial distribution for the number of strings, which is closer to reality than the poissonian one. The results demonstrate good agreement with the asymptotes of the correlation co- eﬃcient analytically calculated earlier at large string density. It is observed that at LHC energy the p t - p t correlation coeﬃcient reveals the drop for most central collisions. The model calculations show that the physical reason for this decrease is the attenuation of color ﬁeld ﬂuctuations due to the string fusion at large string density, whereas at RHIC energy the string density is not enough to provide a decline of the correlation coeﬃcient for most central collisions.

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In this paper we introduce a robust to outliers Wilcoxon change-point testing procedure, for distinguishing between short-**range** dependent time series with a change in **mean** at un- known time and stationary long-**range** dependent time series. We establish the asymptotic distribution of the test statistic under the null hypothesis for L 1 near epoch dependent

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For the first of these studies [9], by Welch at al, the ASH/ ASCO guidelines paper reported the **mean** hemoglobin change for each of the two arms, the experimental and the control. However, they did not report the data for the standard deviation of these means. Since the size of each arm is 15 patients, our formula (16) provides the best esti- mate of the standard deviation using the median and the **range**. We used Figure 1 on page 263 in Welch at al. [9] to estimate the **range** of the hemoglobin change for each arm and used formula (16) to determine the standard devia- tion. The ASH/ASCO guidelines paper also reported the difference in medians of hemoglobin response for the largest study eligible for the meta-analysis conducted by Thatcher at al [10]. Thatcher et al do report in their paper ranges of hemoglobin for patients treated by Epo and con- trol. This trial was a three-arm study, in which two doses of Epo were compared against the control. For the pur- pose of this analysis, we separated the data from each of the Epo arms and compared them against one half of the control group (just like the rest of the studies in the Cochrane review). Using the methods described here, we were able to estimate **mean** increase (using formula (5)) and standard deviation (using **Range**/4 formula in both comparisons). When we incorporated these results into the Cochrane meta-analysis, we found that the effect of Epo on **mean** increase in hemoglobin significantly changed: the pooled estimate decreased from an average of 2.05 g/dl in hemoglobin increase to 1.22 g/dl, i.e., a decrease of approximately 40% (see Figure 3)!

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3 Department of Statistics, QUAID-i-AZAM University, Islamabad, Pakestan.
Abstract. This article presents a formula and a series for approx- imating the normal distribution function. Over the whole **range** of the normal variable z, the proposed formula has the greatest absolute error less than 6.5e − 09, and series has a very high accuracy. We examine the accuracy of our proposed formula and series for various values of z’s. In the sense of accuracy, our formula and series are su- perior to other formulae and series available in the literature. Based on the proposed formula an extended table for the **mean** **range** of the normal variables is established.

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ally utilized by AMC. However, the simplified routes should yield similar outcomes in the fuel burn error to the more complicated routes since the deviations in the more complicated routes account for a small percentage of the total distance, and thus total flight time. The chosen flight routes covered a **range** of different mete- orological phenomena, creating the opportunity for variability between the GFS deterministic and the three ensemble **mean** forecasts. For example, the flight lev- els at which the C-17, C-5, KC-10, and KC-135 cruise ensured that the aircraft passed through the main core of the the polar front jet stream at least once and possibly twice, during the Ramstein AB, Germany to Dover AFB, DE flight. The same can be said for the Joint Base Lewis-McChord, WA to Yokota AB, Japan route. The Travis AFB, CA to Manas AB, Kyrgystan fight route encountered the jet stream twice, once as the aircraft traveled north toward the pole and again af- ter it crossed the pole and traveled south over western Asia. The Charleston AFB, SC to Travis AFB, CA route crossed the Rocky Mountains, another source of vari- ability in the upper-level wind forecasts. Finally, the Travis AFB, CA to Joint Base Pearl Harbor-Hickam, HI route crossed from prevailing mid-latitude westerly winds into tropical easterlies, and in the process, encountered the sub-tropical jet stream.

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In the case of real **range** image data, the output of the tests of four different schemes on four models (Figure 17) shows that the conclusions obtained on synthetic data are valid over the set of real **range** images data. However, when the resolution is very high, the relative error of the scanning process perturbs the accuracy of the Gaussian and the **mean** curvatures values. In this case, the most stable method is Watanabe B for Gaussian curvature and Watanabe A for the **mean** curvature.

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2 INFN, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
3 Dipartimento di Fisica, Universit`a degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy
Abstract. Zero–**range** eﬀective interactions are commonly used in nuclear physics to describe a many-body system in the **mean**-field framework. If they are employed in beyond-**mean**-field models, an artificial ultraviolet divergence is generated by the zero-**range** of the interaction. We analyze this problem in symmetric nuclear matter with the t 0 − t 3 Skyrme model. In this case, the second-order energy correction diverges linearly with the momentum cutoﬀ Λ. After that, we extend the work to the case of nuclear matter with the full Skyrme interaction.

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Abstract. The long-**range** correlation between **mean**-event transverse momenta, being robust against the volume ﬂuctuations and the details of the centrality determination, enables to obtain the signatures of string fusion at the initial stage of hadronic interaction in relativistic heavy ion collisions. The dependence of the correlation strength between **mean**-event transverse momenta on the collision centrality and initial energy is analyzed in a simple model with quark-gluon string fusion on the transverse lattice. It is shown that above RHIC energy the dependence reveals the decline of the correlation coeﬃcient for most central collisions, reﬂecting the attenuation of color ﬁeld ﬂuctuations due to the string fusion at large string density. It is also found that contrary to the correlation between transverse momenta of single particles the strength of the correlation between **mean**-event transverse momenta of particles in two separated rapidity intervals is not decreasing with the total number of produced strings, remaining signiﬁcant even in the case of Pb-Pb collisions, in which the total number of strings can reach several thousand.

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Concluding the Egyptian skulls study
In a previous investigation, you made recommendations to Archie regarding the male Egyptian skulls he discovered at a new site. Your conclusions were based on numerical calculations of **mean**, median, mode, standard deviation and **range**. It is now appropriate to check whether the conclusions drawn at that stage would be consistent with those which might be made on the basis of graphical comparisons.

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increase in process spread using a conventional R chart (control based.. The R chart can be seen to be more sensitive to[r]

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3 Results
In this section, the results obtained from our numerical cal- culation in 208 Pb are discussed. In all cases, we start by solving the HF equations in a radial mesh that extends up to 20 fm, with a radial step of 0.1 fm. Once the HF solu- tion is found, the RPA equations are solved in the usual matrix formulation. Vibrations (or phonons) with a given multipolarity L (see the following sections for more de- tails), and with natural parity, are calculated. The isoscalar dipole state is subtracted using the procedure explained in the Appendix A of Ref. [21]. A lower cuto ﬀ on the col- lectivity of the intermediate phonon states is needed for at least two reasons: firstly, RPA is known to be not reliable for non-collective states, and secondly, introducing poorly collective phonons would oblige to account for the issue of the Pauli principle correction. The RPA model space must be large, due to the zero-**range** character of the Skyrme forces. It consists of all the occupied states, and all the un- occupied states lying below a cuto ﬀ energy E C equal to 50 MeV. The states at positive energy are obtained by setting the system in a box, that is, the continuum is discretized.

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We found that the screening effects resulting from long- **range** intersite interactions affect the impurity spectral func- tions in several ways. In the FL regime, the on-site interaction is weak. The major effect of longer-**range** intersite interactions is to transfer spectral weight from the Hubbard bands to the quasiparticle peak, and to small satellites, which are shifted from the Hubbard bands by roughly the effective screening frequency ν 0 . In the triangle zone, where the on-site interaction is moderate, the longer-**range** intersite interactions can trigger an insulator-metal phase transition. Let us look at Fig. 8(e) , which illustrates the evolution of the spectral functions across such a metal-insulator transition. For the NN case, the system is an insulator with sharp Hubbard bands and sizable gap. However, for the NN + NNN case, spectral weight appears at the Fermi level, which indicates a strongly renormalized metallic state. While the Hubbard bands are smeared out, their position is almost unchanged. When the 3NN intersite interaction is added, the system turns into a good metal with a large quasiparticle peak and the Hubbard bands are shifted to higher energy. In the MI phase in which the on-site interaction is strong, the spectral functions are less affected by longer-**range** intersite interactions. It seems that the longer-**range** intersite interactions do not signiﬁcantly shrink the gaps. The main effect is to redistribute the weight within the Hubbard bands. At the beginning, the upper and lower Hubbard bands are broad and smooth. When longer-**range** intersite interactions are included, the Hubbard bands turn sharper and thinner, and spectral weight is transferred to the edges of the gap and high-frequency features [see Fig. 8(d) ].

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National: IISc, IITM, IMD, NCMRWF International: COLA, NCEP, IPRC, INGV,. APCC, GFDL ,JAMSTEC[r]

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1) Cells throughout the world have variable shapes and sizes. Because of this, and because structure is designed around function, certain shapes are optimal for certain processes. Cell [r]

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DEVELOPING PURPLE WHEAT PURPLE WHEAT AS A SOURCE OF AS A SOURCE OF ANTHOCYANIN PIGMENTS FOR FOOD AND ANTHOCYANIN PIGMENTS FOR FOOD AND ANTHOCYANIN PIGMENTS FOR FOOD AND ANTHOCYANIN PIG[r]

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ABSTRACT
Vitamins are essential nutrients to the body needs in small amount to work properly. The attenuation coefficient is an important parameter for characterizing the penetration and diffusion of x-rays and gamma rays in biological material. The measurement of mass, linear and **mean** free path of biological samples viz. thiamine, adenine, pyridoxine and ascorbic acid in the energies 0.122, 0.356, 0.511, 0.662, 0.840, 1.170, 1.275, 1.330 MeV by using NaI(Tl) scintillation detector. The measured values of mass, linear attenuation coefficient and **mean** free path showed good agreement with theoretical values.

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