In statistics, the mode is the value that appears most often in a set of data values.[1] If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value (i.e, x=argmaxxi P(X = xi)). In other words, it is the value that is most likely to be sampled.
Like the statistical mean and median, the mode is a way of expressing, in a (usually) single number, important information about a random variable or a population. The numerical value of the mode is the same as that of the mean and median in a normal distribution, and it may be very different in highly skewed distributions.
The mode is not necessarily unique to a given discrete distribution since the probability mass function may take the same maximum value at several points x1, x2, etc. The most extreme case occurs in uniform distributions, where all values occur equally frequently.
A mode of a continuous probability distribution is often considered to be any value x at which its probability density function has a locally maximum value.[2] When the probability density function of a continuous distribution has multiple local maxima it is common to refer to all of the local maxima as modes of the distribution, so any peak is a mode. Such a continuous distribution is called multimodal (as opposed to unimodal).
In symmetric unimodal distributions, such as the normal distribution, the mean (if defined), median and mode all coincide. For samples, if it is known that they are drawn from a symmetric unimodal distribution, the sample mean can be used as an estimate of the population mode.
The mode of a sample is the element that occurs most often in the collection. For example, the mode of the sample [1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17] is 6. Given the list of data [1, 1, 2, 4, 4] its mode is not unique. A dataset, in such a case, is said to be bimodal, while a set with more than two modes may be described as multimodal.
For a sample from a continuous distribution, such as [0.935..., 1.211..., 2.430..., 3.668..., 3.874...], the concept is unusable in its raw form, since no two values will be exactly the same, so each value will occur precisely once. In order to estimate the mode of the underlying distribution, the usual practice is to discretize the data by assigning frequency values to intervals of equal distance, as for making a histogram, effectively replacing the values by the midpoints of theintervals they are assigned to. The mode is then the value where the histogram reaches its peak. For small or middle-sized samples the outcome of this procedure is sensitive to the choice of interval width if chosen too narrow or too wide; typically one should have a sizable fraction of the data concentrated in a relatively small number of intervals (5 to 10), while the fraction of the data falling outside these intervals is also sizable. An alternate approach is kernel density estimation, which essentially blurs point samples to produce a continuous estimate of the probability density function which can provide an estimate of the mode.
Unlike mean and median, the concept of mode also makes sense for "nominal data" (i.e., not consisting of numerical values in the case of mean, or even of ordered values in the case of median). For example, taking a sample of Korean family names, one might find that "Kim" occurs more often than any other name. Then "Kim" would be the mode of the sample. In any voting system where a plurality determines victory, a single modal value determines the victor, while a multi-modal outcome would require some tie-breaking procedure to take place.
Unlike median, the concept of mode makes sense for any random variable assuming values from a vector space, including the real numbers (a one-dimensional vector space) and the integers (which can be considered embedded in the reals). For example, a distribution of points in the plane will typically have a mean and a mode, but the concept of median does not apply. The median makes sense when there is a linear order on the possible values. Generalizations of the concept of median to higher-dimensional spaces are the geometric median and the centerpoint.
For some probability distributions, the expected value may be infinite or undefined, but if defined, it is unique. The mean of a (finite) sample is always defined. The median is the value such that the fractions not exceeding it and not falling below it are each at least 1/2. It is not necessarily unique, but never infinite or totally undefined. For a data sample it is the "halfway" value when the list of values is ordered in increasing value, where usually for a list of even length the numerical average is taken of the two values closest to "halfway". Finally, as said before, the mode is not necessarily unique. Certain pathological distributions (for example, the Cantor distribution) have no defined mode at all.[citation needed][4] For a finite data sample, the mode is one (or more) of the values in the sample.
Pearson uses the term mode interchangeably with maximum-ordinate. In a footnote he says, "I have found it convenient to use the term mode for the abscissa corresponding to the ordinate of maximum frequency."
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A PersistentVolumeClaim (PVC) is a request for storage by a user. It is similarto a Pod. Pods consume node resources and PVCs consume PV resources. Pods canrequest specific levels of resources (CPU and Memory). Claims can request specificsize and access modes (e.g., they can be mounted ReadWriteOnce, ReadOnlyMany,ReadWriteMany, or ReadWriteOncePod, see AccessModes).
While PersistentVolumeClaims allow a user to consume abstract storage resources,it is common that users need PersistentVolumes with varying properties, such asperformance, for different problems. Cluster administrators need to be able tooffer a variety of PersistentVolumes that differ in more ways than size and accessmodes, without exposing users to the details of how those volumes are implemented.For these needs, there is the StorageClass resource.
A user creates, or in the case of dynamic provisioning, has already created,a PersistentVolumeClaim with a specific amount of storage requested and withcertain access modes. A control loop in the control plane watches for new PVCs, findsa matching PV (if possible), and binds them together. If a PV was dynamicallyprovisioned for a new PVC, the loop will always bind that PV to the PVC. Otherwise,the user will always get at least what they asked for, but the volume may be inexcess of what was requested. Once bound, PersistentVolumeClaim binds are exclusive,regardless of how they were bound. A PVC to PV binding is a one-to-one mapping,using a ClaimRef which is a bi-directional binding between the PersistentVolumeand the PersistentVolumeClaim.
Pods use claims as volumes. The cluster inspects the claim to find the boundvolume and mounts that volume for a Pod. For volumes that support multipleaccess modes, the user specifies which mode is desired when using their claimas a volume in a Pod.
When a volume contains a file system, the file system is only resized when a new Pod is usingthe PersistentVolumeClaim in ReadWrite mode. File system expansion is either done when a Pod is starting upor when a Pod is running and the underlying file system supports online expansion.
You can set the value of volumeMode to Block to use a volume as a raw block device.Such volume is presented into a Pod as a block device, without any filesystem on it.This mode is useful to provide a Pod the fastest possible way to access a volume, withoutany filesystem layer between the Pod and the volume. On the other hand, the applicationrunning in the Pod must know how to handle a raw block device.See Raw Block Volume Supportfor an example on how to use a volume with volumeMode: Block in a Pod.
A PersistentVolume can be mounted on a host in any way supported by the resourceprovider. As shown in the table below, providers will have different capabilitiesand each PV's access modes are set to the specific modes supported by that particularvolume. For example, NFS can support multiple read/write clients, but a specificNFS PV might be exported on the server as read-only. Each PV gets its own set ofaccess modes describing that specific PV's capabilities.
If a user requests a raw block volume by indicating this using the volumeModefield in the PersistentVolumeClaim spec, the binding rules differ slightly fromprevious releases that didn't consider this mode as part of the spec.Listed is a table of possible combinations the user and admin might specify forrequesting a raw block device. The table indicates if the volume will be bound ornot given the combinations: Volume binding matrix for statically provisioned volumes:
Maintenance Mode was successfully trialed on the Galaxy S21 series in Korea in July and then launched in China in September 2022. It launches globally today, gradually rolling out over the next few months on select models running One UI 5. The rollout will continue throughout 2023, with availability expanding to more Galaxy devices. Stay tuned for more information on local availability.
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