WordNet

let eat; "range the animals in the prairie"
a place for shooting (firing or driving) projectiles of various kinds; "the army maintains a missile range in the desert"; "any good golf club will have a range where you can practice"
a series of hills or mountains; "the valley was between two ranges of hills"; "the plains lay just beyond the mountain range" (同)mountain_range, range of mountains, chain, mountain_chain, chain of mountains
the limits within which something can be effective; "range of motion"; "he was beyond the reach of their fire" (同)reach
a large tract of grassy open land on which livestock can graze; "they used to drive the cattle across the open range every spring"; "he dreamed of a home on the range"
a variety of different things or activities; "he answered a range of questions"; "he was impressed by the range and diversity of the collection"
lay out orderly or logically in a line or as if in a line; "lay out the clothes"; "lay out the arguments" (同)array, lay_out, set out
change or be different within limits; "Estimates for the losses in the earthquake range as high as $2 billion"; "Interest rates run from 5 to 10 percent"; "The instruments ranged from tuba to cymbals"; "My students range from very bright to dull" (同)run
range or extend over; occupy a certain area; "The plants straddle the entire state" (同)straddle
have a range; be capable of projecting over a certain distance, as of a gun; "This gun ranges over two miles"
wandering freely; "at night in bed...his slowly ranging thoughts...encountered her"

PrepTutorEJDIC

〈U〉《時にa~》(価格・気温などの変動の)『幅』 / 〈U〉《時にa~》(知覚・知識などの)『範囲』,広がり / 〈U〉《時にa~》(銃砲・ミサイルなどの)着弾距離,射程 / 〈U〉《時a~》(航空機・船舶などの)航続距離 / 〈C〉(銃砲の)射撃場,(ミサイルナドの)試射場 / 〈C〉《米》放牧地域 / 〈C〉(山などの)列,連なり / 〈C〉(料理用の)レンジ / 〈U〉《しばしばa~》(動植物の)生息(分布)区域 / 《副詞句を伴って》(価格・気温などがある範囲内で)『変動する』,動く / (…を)さまよう,歩き回る,(…に)及ぶ《+『over』(『through』)+『名』》 / 一列(一直線)に延びている / (動植物が)分布している / 《副詞[句]を伴って》(ある状態に)…‘を'『並べて置く』,配列する,整列させる / …‘を'さまよう,歩き回る(受動態にできない) / 《米》〈家畜〉‘を'放牧地に入れる
runの過去形
ringの過去

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/06/15 03:45:07」(JST)

wiki en

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 upper and lower quartiles,^[1]^[2] IQR = Q₃ − Q₁. It is a trimmed estimator, defined as the 25% trimmed mid-range, and is the most significant basic robust measure of scale. It is the 3rd Quartile of a box plot plot minus the first quartile.

Use[edit]

Unlike (total) range, the interquartile range has 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 (where 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.

Filtering of outliers (see below).

Examples[edit]

Boxplot (with an interquartile range) and a probability density function (pdf) of a Normal

N(0,σ 2)

Population

Data set in a table[edit]

i	x[i]	Quartile
1	102
2	104
3	105	Q₁
4	107
5	108
6	109	Q₂ (median)
7	110
8	112
9	115	Q₃
10	116
11	118

For the data in this table the interquartile range is IQR = 115 − 105 = 10.

Data set in a plain-text box plot[edit]

                    
                             +-----+-+     
   o           *     |-------|     | |---|
                             +-----+-+    
                    
 +---+---+---+---+---+---+---+---+---+---+---+---+   number line
 0   1   2   3   4   5   6   7   8   9   10  11  12

For the data set in this box plot:

lower (first) quartile Q₁ = 7
median (second quartile) Q₂ = 8.5
upper (third) quartile Q₃ = 9
interquartile range, IQR = Q₃ − Q₁ = 2

Interquartile range of distributions[edit]

The interquartile range of a continuous distribution can be calculated by integrating the probability density function (which yields the cumulative distribution function — any other means of calculating the CDF will also work). The lower quartile, Q₁, is a number such that integral of the PDF from -∞ to Q₁ equals 0.25, while the upper quartile, Q₃, is such a number that the integral from -∞ to Q₃ equals 0.75; in terms of the CDF, the quartiles can be defined as follows:

where CDF⁻¹ is the quantile function.

The interquartile range and median of some common distributions are shown below

Distribution	Median	IQR
Normal	μ	2 Φ⁻¹(0.75)σ ≈ 1.349σ
Laplace	μ	2b ln(2) ≈ 1.386b
Cauchy	μ	2γ

Interquartile range test for normality of distribution[edit]

The IQR, mean, and standard deviation of a population P can be used in a simple test of whether or not P is normally distributed, or Gaussian. If P is normally distributed, then the standard score of the first quartile, z₁, is -0.67, and the standard score of the third quartile, z₃, is +0.67. Given mean = X and standard deviation = σ for P, if P is normally distributed, the first quartile

and the third quartile

If the actual values of the first or third quartiles differ substantially^{[clarification needed]} from the calculated values, P is not normally distributed.

Interquartile range and outliers[edit]

Figure 3. Box-and-whisker plot with four close and one far away extreme values, defined as outliers above Q3 + 1.5(IQR) and Q3 + 3(IQR), respectively.

The interquartile range is often used to find outliers in data. Outliers are observations that fall below Q1 - 1.5(IQR) or above Q3 + 1.5(IQR). In a boxplot, the highest and lowest occurring value within this limit are drawn as bar of the whiskers, and the outliers as individual points.

References[edit]

^ Upton, Graham; Cook, Ian (1996). Understanding Statistics. Oxford University Press. p. 55. ISBN 0-19-914391-9.
^ Zwillinger, D., Kokoska, S. (2000) CRC Standard Probability and Statistics Tables and Formulae, CRC Press. ISBN 1-58488-059-7 page 18.

UpToDate Contents

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English Journal

High cortisol levels are associated with cognitive impairment no-dementia (CIND) and dementia.

Lara VP, Caramelli P, Teixeira AL, Barbosa MT, Carmona KC, Carvalho MG, Fernandes AP, Gomes KB.SourceDepartamento de Análises Clínicas e Toxicológicas, Faculdade de Farmácia, Universidade Federal de Minas Gerais, Belo Horizonte 31270-901, Brazil.
Clinica chimica acta; international journal of clinical chemistry.Clin Chim Acta.2013 Aug 23;423:18-22. doi: 10.1016/j.cca.2013.04.013. Epub 2013 Apr 20.
BACKGROUND: This study aimed to compare serum cortisol concentrations in cognitively healthy elderly and in subjects with cognitive impairment no dementia (CIND) and dementia, besides to evaluate these concentrations according to apolipoprotein E genotype (APOE).METHODS: Three-hundred and nine elder
PMID 23611893

Combined use of exercise electrocardiography, coronary calcium score and cardiac CT angiography for the prediction of major cardiovascular events in patients presenting with stable chest pain.

Versteylen MO, Joosen IA, Winkens MH, Laufer EM, Snijder RJ, Wildberger JE, Crijns HJ, Narula J, Hofstra L.SourceDepartment of Cardiology, Maastricht University Medic\al Center, Maastricht, The Netherlands. Electronic address: mathijs.versteylen@mumc.nl.
International journal of cardiology.Int J Cardiol.2013 Jul 15;167(1):121-5. doi: 10.1016/j.ijcard.2011.12.016. Epub 2012 Jan 5.
BACKGROUND: The usual diagnostic work-up of chest pain patients includes clinical risk profiling and exercise-ECG, possibly followed by additional tests. Recently cardiac computed tomographic angiography (CCTA) has been employed. We evaluated the prognostic value of the combined use of exercise-ECG
PMID 22225760

Clinical response, drug survival and predictors thereof in 432 ankylosing spondylitis patients after switching tumour necrosis factor α inhibitor therapy: results from the Danish nationwide DANBIO registry.

Glintborg B, Ostergaard M, Krogh NS, Tarp U, Manilo N, Loft AG, Hansen A, Schlemmer A, Fana V, Lindegaard HM, Nordin H, Rasmussen C, Ejstrup L, Jensen DV, Petersen PM, Hetland ML.SourceDepartment of Rheumatology, Gentofte University Hospital, Copenhagen, Denmark.
Annals of the rheumatic diseases.Ann Rheum Dis.2013 Jul;72(7):1149-55. doi: 10.1136/annrheumdis-2012-201933. Epub 2012 Aug 31.
OBJECTIVE: To investigate frequencies and reasons for switching, treatment responses and drug survival in patients with ankylosing spondylitis (AS) switching tumour-necrosis-factor-α inhibitor (TNFi) treatment in routine clinical care.METHODS: AS patients were identified in the Danish nationwide DA
PMID 22941767

Japanese Journal

Investigation of Bispectral Index Asymmetry in Patients with Cerebral Infarction

Sawada Masahiro,Yoshida Hitoshi,Hirota Kazuyoshi
弘前医学 65(2-4), 156-163, 2014-09-30
… The median CI duration was 48 months （interquartile range, 23–96）. …
NAID 120005496548

Clinical impact of albuminuria and glomerular filtration rate on renal and cardiovascular events, and all-cause mortality in Japanese patients with type 2 diabetes

Wada Takashi,Haneda Masakazu,Furuichi Kengo,Babazono Tetsuya,Yokoyama Hiroki,Iseki Kunitoshi,Araki Shin-ichi,Ninomiya Toshiharu,Hara Shigeko,Suzuki Yoshiki,Iwano Masayuki,Kusano Eiji,Moriya Tatsumi,Satoh Hiroaki,Nakamura Hiroyuki,Shimizu Miho,Toyama Tadashi,Hara Akinori,Makino Hirofumi
Clinical and Experimental Nephrology 18(4), 613-620, 2014-08
… Results: During follow-up (median 7.0 years, interquartile range 3.0-8.0 years), 419 renal events, 605 cardiovascular events and 236 deaths occurred. …
NAID 120005411654

病院に勤務する男性看護師のSOC，ストレス反応，SOCとストレス反応との関連

吉田えり,山田和子,森岡郁晴
産業衛生学雑誌 56(5), 152-161, 2014
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NAID 130004699262