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57-446: On August 17, the fire, three miles south of Salinas, spread to 2,800 acres and threatened 1,500 structures; four firefighters were injured. The fire had burned 4,070 acres by August 18, and as of August 19, the fire had grown to over 10,000 acres. By August 21, over 42,000 acres had burned and the fire was 12% contained. The nearby Carmel Fire was over 5,069 acres and five percent contained. On September 4, Cal Fire reported that both

114-447: A ↦ E ⁡ ( ‖ X − a ‖ ) . {\displaystyle a\mapsto \operatorname {E} (\|X-a\|).\,} The spatial median is unique when the data-set's dimension is two or more. An alternative proof uses the one-sided Chebyshev inequality; it appears in an inequality on location and scale parameters . This formula also follows directly from Cantelli's inequality . For

171-763: A probability density function f ), nor does it require a discrete one . In the former case, the inequalities can be upgraded to equality: a median satisfies P ⁡ ( X ≤ m ) = ∫ − ∞ m f ( x ) d x = 1 2 {\displaystyle \operatorname {P} (X\leq m)=\int _{-\infty }^{m}{f(x)\,dx}={\frac {1}{2}}} and P ⁡ ( X ≥ m ) = ∫ m ∞ f ( x ) d x = 1 2 . {\displaystyle \operatorname {P} (X\geq m)=\int _{m}^{\infty }{f(x)\,dx}={\frac {1}{2}}\,.} Any probability distribution on

228-523: A CAL FIRE S-2T air tanker crashed while fighting the Dog Rock Fire in Yosemite National Park . The pilot was killed. CAL FIRE uses several enterprise IT systems to manage operations. Altaris CAD, a computer-assisted dispatch system made by Northrop Grumman , is employed by each unit's emergency command center (ECC) to track available resources and assignments. This is made possible through

285-404: A comment on a subsequent proof by O'Cinneide, Mallows in 1991 presented a compact proof that uses Jensen's inequality twice, as follows. Using |·| for the absolute value , we have The first and third inequalities come from Jensen's inequality applied to the absolute-value function and the square function, which are each convex. The second inequality comes from the fact that a median minimizes

342-404: A median grade when student test scores are graded from F to A), although the result might be halfway between classes if there is an even number of classes. (For odd number classes, one specific class is determined as the median.) A geometric median , on the other hand, is defined in any number of dimensions. A related concept, in which the outcome is forced to correspond to a member of the sample,

399-408: A median is based on the middle data in a set, it is not necessary to know the value of extreme results in order to calculate it. For example, in a psychology test investigating the time needed to solve a problem, if a small number of people failed to solve the problem at all in the given time a median can still be calculated. Because the median is simple to understand and easy to calculate, while also

456-430: A median is defined as any real number  m that satisfies the inequalities lim x → m − F ( x ) ≤ 1 2 ≤ F ( m ) {\displaystyle \lim _{x\to m-}F(x)\leq {\frac {1}{2}}\leq F(m)} (cf. the drawing in the definition of expected value for arbitrary real-valued random variables ). An equivalent phrasing uses

513-501: A random variable X distributed according to F : P ⁡ ( X ≤ m ) ≥ 1 2  and  P ⁡ ( X ≥ m ) ≥ 1 2 . {\displaystyle \operatorname {P} (X\leq m)\geq {\frac {1}{2}}{\text{ and }}\operatorname {P} (X\geq m)\geq {\frac {1}{2}}\,.} Note that this definition does not require X to have an absolutely continuous distribution (which has

570-410: A robust approximation to the mean , the median is a popular summary statistic in descriptive statistics . In this context, there are several choices for a measure of variability : the range , the interquartile range , the mean absolute deviation , and the median absolute deviation . For practical purposes, different measures of location and dispersion are often compared on the basis of how well

627-424: A single pass over the sample. The distributions of both the sample mean and the sample median were determined by Laplace . The distribution of the sample median from a population with a density function f ( x ) {\displaystyle f(x)} is asymptotically normal with mean μ {\displaystyle \mu } and variance where m {\displaystyle m}

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684-410: A statistical distribution : it is the 2nd quartile , 5th decile , and 50th percentile . The median can be used as a measure of location when one attaches reduced importance to extreme values, typically because a distribution is skewed , extreme values are not known, or outliers are untrustworthy, i.e., may be measurement or transcription errors. For example, consider the multiset The median

741-473: A well-defined mean, such as the Cauchy distribution : The mean absolute error of a real variable c with respect to the random variable   X is Provided that the probability distribution of X is such that the above expectation exists, then m is a median of X if and only if m is a minimizer of the mean absolute error with respect to X . In particular, if m is a sample median, then it minimizes

798-590: A wide range of disasters and incidents, including earthquakes, water rescues, and hazardous material spills. The organization manages eight Demonstration State Forests for timber production, recreation, and research. In conjunction with the California Department of Corrections and Rehabilitation , CAL FIRE uses thousands of incarcerated firefighters at 44 conservation camps throughout the state on fire prevention, fire suppression, and various maintenance and conservation projects. CAL FIRE works with employees of

855-486: A young convict volunteers for the Conservation Camp Program and assists Cal Fire. [REDACTED] Media related to California Department of Forestry and Fire Protection at Wikimedia Commons Median The median of a set of numbers is the value separating the higher half from the lower half of a data sample , a population , or a probability distribution . For a data set , it may be thought of as

912-470: Is 2 in this case, as is the mode , and it might be seen as a better indication of the center than the arithmetic mean of 4, which is larger than all but one of the values. However, the widely cited empirical relationship that the mean is shifted "further into the tail" of a distribution than the median is not generally true. At most, one can say that the two statistics cannot be "too far" apart; see § Inequality relating means and medians below. As

969-530: Is a stub . You can help Misplaced Pages by expanding it . Cal Fire The California Department of Forestry and Fire Protection ( CAL FIRE ) is the fire department of the California Natural Resources Agency in the U.S. state of California . It is responsible for fire protection in various areas under state responsibility totaling 31 million acres, as well as the administration of the state's private and public forests . In addition,

1026-469: Is a C function, but the reverse does not hold. If f is a C function, then If the medians are not unique, the statement holds for the corresponding suprema. Even though comparison-sorting n items requires Ω ( n log n ) operations, selection algorithms can compute the k th-smallest of n items with only Θ( n ) operations. This includes the median, which is the ⁠ n / 2 ⁠ th order statistic (or for an even number of samples,

1083-426: Is greater than or equal to the proposed median. As seen above, medians may not be unique. If each set contains more than half the population, then some of the population is exactly equal to the unique median. The median is well-defined for any ordered (one-dimensional) data and is independent of any distance metric . The median can thus be applied to school classes which are ranked but not numerical (e.g. working out

1140-424: Is less than the mean, as shown in the figure. Jensen's inequality states that for any random variable X with a finite expectation E [ X ] and for any convex function f This inequality generalizes to the median as well. We say a function f : R → R is a C function if, for any t , is a closed interval (allowing the degenerate cases of a single point or an empty set ). Every convex function

1197-564: Is managed from an office in Davis, California . The largest and most visible part of CAL FIRE operations is fire protection. Operations are divided into 21 operational units, which geographically follow county lines. Each unit consists of the area of one or more counties. Operational units are grouped under either the North Region or South Region. The Office of the State Fire Marshal (OSFM)

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1254-677: Is planning to acquire up to 12 of these rotorcraft to replace the aging Bell UH-1H Super Huey fleet. From the 13 air attack and ten 10 helitack bases located statewide, aircraft can reach most fires within 20 minutes. Aircraft are a prominent feature of CAL FIRE, especially during the summer fire season. Both fixed- and rotary-wing aircraft are employed. Helicopters (also known as rotorcraft or rotary wing aircraft) are used to transport firefighting "Helitack Crews" into fire areas. They also drop water and retardant chemicals on fires. Fixed-wing aircraft are used for command , observation, and to drop retardant chemicals on fires. CAL FIRE contracted in

1311-410: Is the medoid . There is no widely accepted standard notation for the median, but some authors represent the median of a variable x as med( x ), x͂ , as μ 1/2 , or as M . In any of these cases, the use of these or other symbols for the median needs to be explicitly defined when they are introduced. The median is a special case of other ways of summarizing the typical values associated with

1368-820: Is the CAL FIRE Training Center in Ione , east of Sacramento. The second academy is at the Ben Clark Training Center in Riverside . Both centers host the Fire Fighter Academy (FFA). All CAL FIRE Fire Protection employees go through this academy once they become permanent employees. The Company Officer Academy (COA) is only held in Ione. All new company officers (Engineer, Captain, Forester I, etc.) attend this academy. The uniformed executive staff of CAL FIRE includes

1425-486: Is the CAL FIRE program that protects life and property through the development and application of fire prevention, engineering, training and education, and enforcement. As part of this mission, OSFM establishes a fire-safe environment for the people of California, which serves as a foundation for local agencies to build on as they strive to meet their specific goals. There are two CAL FIRE training centers. The original academy

1482-520: Is the median of f ( x ) {\displaystyle f(x)} and n {\displaystyle n} is the sample size: A modern proof follows below. Laplace's result is now understood as a special case of the asymptotic distribution of arbitrary quantiles . For normal samples, the density is f ( m ) = 1 / 2 π σ 2 {\displaystyle f(m)=1/{\sqrt {2\pi \sigma ^{2}}}} , thus for large samples

1539-401: Is uncontaminated by data from heavy-tailed distributions or from mixtures of distributions. Even then, the median has a 64% efficiency compared to the minimum-variance mean (for large normal samples), which is to say the variance of the median will be ~50% greater than the variance of the mean. For any real -valued probability distribution with cumulative distribution function   F ,

1596-562: The California Conservation Corps since that agency's creation in a partnership for fire suppression duties, logistics and forestry management. CCC members are involved in job training programs as Type 1 Hand Crew firefighters, supervised by CAL FIRE personnel, in increasing prevalence to offset CDCR inmates as the incarcerated firefighter program is closed. Programs to control wood boring insects and diseases of trees are under forestry programs managed by CAL FIRE. The vehicle fleet

1653-645: The Inland Empire and communities in the metropolitan Palm Springs area. The area includes forested mountains, the Colorado River basin, the Mojave Desert and Interstate 10 . The counties of Marin (MRN), Kern (KRN), Santa Barbara (SBC), Ventura (VNC), Los Angeles (LAC) and Orange (ORC) are paid by CAL FIRE to provide fire protection to state responsibility areas within those counties rather than CAL FIRE providing direct fire protection, and are commonly known as

1710-679: The International Association of Firefighters (IAFF). Operational units are organizations designed to address fire suppression over a geographic area. They vary widely in size and terrain . For example, Lassen-Modoc-Plumas Operational Unit encompasses three rural counties and consists of eight fire stations, one Helitack Base, three conservation camps and an inmate firefighter training center. Fire suppression resources include 13 front-line fire engines, 1 helicopter, 3 bulldozers and 14 inmate fire crews. The unit shares an interagency emergency command center with federal agencies including

1767-558: The US Forest Service , National Park Service , and the Bureau of Land Management . An interagency center contributes to economies of scale, supports cooperation, and lends itself to a more seamless operation. The area has fragmented jurisdictions across a large rural area along the Nevada and Oregon state lines. Riverside Operational Unit by itself is one of the largest fire departments in

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1824-410: The absolute deviation function a ↦ E ⁡ ( | X − a | ) {\displaystyle a\mapsto \operatorname {E} (|X-a|)} . Mallows's proof can be generalized to obtain a multivariate version of the inequality simply by replacing the absolute value with a norm : where m is a spatial median , that is, a minimizer of the function

1881-422: The arithmetic mean of the two middle order statistics). Selection algorithms still have the downside of requiring Ω( n ) memory, that is, they need to have the full sample (or a linear-sized portion of it) in memory. Because this, as well as the linear time requirement, can be prohibitive, several estimation procedures for the median have been developed. A simple one is the median of three rule, which estimates

1938-514: The "Contract Counties". Lawmakers in Sacramento have mandated that every operational unit develop and implement an annual fire management plan. The plan will develop cooperation and community programs to reduce damage from, and costs of, fires in California. One metric used by fire suppression units is initial attack success: fires stopped by the initial resources, (equipment and people,) sent to

1995-531: The CAL FIRE Web site under Mobile Equipment. CAL FIRE owns its own fleet of air tankers, tactical aircraft and helicopters, which are managed under the Aviation Management Program. Additional aviation resources are leased by the department when needed. All of the fixed wing aircraft, while owned by CAL FIRE, are piloted and maintained by DynCorp International. The CAL FIRE Air Program is one of

2052-556: The Model 14, and 15. CAL FIRE Models 24 and 25 were test-bed models, with only a few of each model fielded. The newest versions of these engines are CAL FIRE model 34 (4WD) and 35 (2WD), manufactured by Placer Fire Equipment , Rosenbauer , and HME . Model 34/35's are currently being fielded statewide. As of 2009 Model 35's have been discontinued and Model 34's from BME Apparatus are the new standard. Fact sheets on all of CAL FIRE's current-service Type 3 (wildland) engine models can be found on

2109-603: The River Fire and the Carmel Fire were 100% contained. The River Fire had burned 48,088 acres and the Carmel Fire had burned 6,905 acres; between them, they had destroyed 103 structures and damaged 20. When a strong atmospheric river winter storm came to the burned area in January, 2021, a mudslide occurred and damaged homes and barns near River Road, and trapped several horses that were later rescued. This wildfire -related article

2166-453: The arithmetic mean of the absolute deviations. Note, however, that in cases where the sample contains an even number of elements, this minimizer is not unique. More generally, a median is defined as a minimum of as discussed below in the section on multivariate medians (specifically, the spatial median ). This optimization-based definition of the median is useful in statistical data-analysis, for example, in k -medians clustering . If

2223-576: The case of unimodal distributions, one can achieve a sharper bound on the distance between the median and the mean: A similar relation holds between the median and the mode: A typical heuristic is that positively skewed distributions have mean > median. This is true for all members of the Pearson distribution family . However this is not always true. For example, the Weibull distribution family has members with positive mean, but mean < median. Violations of

2280-436: The corresponding population values can be estimated from a sample of data. The median, estimated using the sample median, has good properties in this regard. While it is not usually optimal if a given population distribution is assumed, its properties are always reasonably good. For example, a comparison of the efficiency of candidate estimators shows that the sample mean is more statistically efficient when—and only when— data

2337-665: The department provides varied emergency services in 36 of the state's 58 counties via contracts with local governments. The department's current director is Joe Tyler, who was appointed March 4, 2022, by Governor of California Gavin Newsom . CAL FIRE's foremost operational role is to fight and prevent wildfire on 31 million acres of state forestland. The organization works in both suppression and prevention capacities on state land, and offers emergency services of various kinds in 36 out of California's 58 counties, through contracts with local governments. The organization also assists in response to

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2394-412: The distribution has finite variance, then the distance between the median X ~ {\displaystyle {\tilde {X}}} and the mean X ¯ {\displaystyle {\bar {X}}} is bounded by one standard deviation . This bound was proved by Book and Sher in 1979 for discrete samples, and more generally by Page and Murty in 1982. In

2451-637: The following individuals. As of 2017, median pay for full time firefighters (which includes base pay, special pay, overtime and benefits) is $ 148,000. Firefighters employed by the California Department of Forestry and Fire Protection are represented by IAFF affiliate, CAL FIRE Local 2881, which represents 5,700 members within CAL FIRE Local 2881 and is also associated with the California Professional Firefighters (CPF) and

2508-470: The formula for the case of discrete variables is given below in § Empirical local density . The sample can be summarized as "below median", "at median", and "above median", which corresponds to a trinomial distribution with probabilities F ( v ) {\displaystyle F(v)} , f ( v ) {\displaystyle f(v)} and 1 − F ( v ) {\displaystyle 1-F(v)} . For

2565-448: The incident. CAL FIRE uses various apparatus to accomplish their daily responses. Engines fall under two categories, either being state-owned — mostly wildland, or city/county owned, which CAL FIRE operates under contract. For the wildland portion, most engines are manufactured with West-Mark or Westates (now American Truck & Fire Apparatus) bodies on an International chassis. Commonly seen models of wildland engines include

2622-437: The largest incomes alone have no effect on the median. For this reason, the median is of central importance in robust statistics . The median of a finite list of numbers is the "middle" number, when those numbers are listed in order from smallest to greatest. If the data set has an odd number of observations, the middle one is selected (after arranging in ascending order). For example, the following list of seven numbers, has

2679-585: The largest non-military air programs in the country, consisting of 23 Grumman S-2 Tracker (S-2T version) 1,200 gallon fixed wing turboprop air tankers, seven Lockheed-Martin C-130H Hercules 4,000 gallon fixed-wing turboprop air tankers (in service in 2025), 14 North American Rockwell OV-10 Bronco fixed wing turboprop air tactical aircraft and 12 Bell UH-1H Super Huey helicopters. CAL FIRE has also now begun operating new Sikorsky S-70i Firehawk helicopters for aerial firefighting support including water drops and

2736-435: The median as the fully trimmed mid-range ). In general, with this convention, the median can be defined as follows: For a data set x {\displaystyle x} of n {\displaystyle n} elements, ordered from smallest to greatest, Formally, a median of a population is any value such that at least half of the population is less than or equal to the proposed median and at least half

2793-459: The median as the median of a three-element subsample; this is commonly used as a subroutine in the quicksort sorting algorithm, which uses an estimate of its input's median. A more robust estimator is Tukey 's ninther , which is the median of three rule applied with limited recursion: if A is the sample laid out as an array , and then The remedian is an estimator for the median that requires linear time but sub-linear memory, operating in

2850-431: The median of 6 , which is the fourth value. If the data set has an even number of observations, there is no distinct middle value and the median is usually defined to be the arithmetic mean of the two middle values. For example, this data set of 8 numbers has a median value of 4.5 , that is ( 4 + 5 ) / 2 {\displaystyle (4+5)/2} . (In more technical terms, this interprets

2907-608: The nation, with 95 fire stations and about 230 pieces of equipment. The Riverside Operational Unit operates the Riverside County Fire Department under contract as well operates eighteen city fire departments and one community services district fire department. Nine of these stations belong to the state, with rest owned by the respective local government entity. The unit operates its own emergency command center in Perris . Terrain served includes urban and suburban areas of

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2964-451: The past with 10 Tanker Air Carrier for three years' of exclusive use of their McDonnell Douglas DC-10-10 heavy air tanker known as Tanker 910 for aerial firefighting at a cost of $ 5 million per year. Additional access was also provided to DC-10-30 air tankers, being Tanker 911 and Tanker 912. In 2014 Tanker 910 was retired; however, 10 Tanker Air Carrier continues to currently operate several DC-10-30 air tankers. On October 7, 2014,

3021-430: The real number set R {\displaystyle \mathbb {R} } has at least one median, but in pathological cases there may be more than one median: if F is constant 1/2 on an interval (so that f = 0 there), then any value of that interval is a median. The medians of certain types of distributions can be easily calculated from their parameters; furthermore, they exist even for some distributions lacking

3078-400: The rule are particularly common for discrete distributions. For example, any Poisson distribution has positive skew, but its mean < median whenever μ mod 1 > ln ⁡ 2 {\displaystyle \mu {\bmod {1}}>\ln 2} . See for a proof sketch. When the distribution has a monotonically decreasing probability density, then the median

3135-405: The use of an automatic vehicle locating (AVL) system which provides vehicle location, data communication, and dispatching through a mobile data terminal (MDT) and a multi-network switching system in over 1200 vehicles statewide. Each operational unit has a stand-alone system which includes detailed address and mapping information. Fire Country is an American drama television series in which

3192-420: The variance of the median equals ( π / 2 ) ⋅ ( σ 2 / n ) . {\displaystyle ({\pi }/{2})\cdot (\sigma ^{2}/n).} (See also section #Efficiency below.) We take the sample size to be an odd number N = 2 n + 1 {\displaystyle N=2n+1} and assume our variable continuous;

3249-403: The “middle" value. The basic feature of the median in describing data compared to the mean (often simply described as the "average") is that it is not skewed by a small proportion of extremely large or small values, and therefore provides a better representation of the center. Median income , for example, may be a better way to describe the center of the income distribution because increases in

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