Question

discuss the sensitivity of outliers for mean, median, interquartile range, range, variance and standar deviation

Answer 1

Answer:

• mean:  
• A central distinction among mean and middle is that the mean is substantially more delicate to extraordinary qualities than the middle. That is, a couple of outrageous qualities can change the mean a considerable measure however don't change the middle in particular. In this way, the middle is more strong (less touchy to anomalies in the information) than the mean.
• formula for mean: μ = ( Σ Xi ) / N
• Means' "sensibility" to data is actually one of the reasons why we choose it as a estimator of location. Obviously, if one or more of the values deviate from the other, they influence the mean. If they deviate by large, their influence is larger, if deviation is smaller, than their influence is smaller. It is true that "small amount of observations shouldn't have much impact" on it's result, but that doesn't mean that they have no impact.
• median:
• A fundamental difference between mean and median is that the mean is much more sensitive to extreme values than the median. That is, one or two extreme values can change the mean a lot but do not change the the median very much. Thus, the median is more robust (less sensitive to outliers in the data) than themean.
• Median=(n+1n)thterm

Interquartile range:

• the interquartile run is based upon the computation of different measurements. Before deciding the interquartile go, we first need to know the estimations of the main quartile and third quartile. (Obviously the first and third quartiles rely on the estimation of the middle).
• When we have decided the estimations of the first and third quartiles, the interquartile extend is anything but difficult to ascertain. Everything that we need to do is to subtract the principal quartile from the third quartile. This clarifies the utilization of the term interquartile run for this measurement.
• Range:
• conveyance as figured by subtracting the littlest incentive from the biggest incentive in the informational collection. The range is touchy to exceptions. The interquartile extend is the width as estimated from the lower quartile to the upper quartile of an appropriation. Basically, the lower quartile is the middle of the lower half appropriation of the information extending from the lower extraordinary to the middle of the first dissemination, and the upper quartile is the middle of the upper portion of the first circulation. The interquartile extend runs with the middle and dissimilar to the range, it is vigorous against exceptions, as in a couple of anomalies don't change the outcomes in particular. The standard deviation is a conventional proportion of changeability and is the best acknowledged and most generally utilized of all fluctuation measures. For an example of information, the example standard deviation or the standard deviation of the example is computed by the equation
• formula for range is MAXIMUM- MINIMUM

Variance:

• Variance measures how far a data set is spread out. The technical definition is “The average of the squared differences from the mean,” but all it really does is to give you a very general idea of the spread of your data. A value of zero means that there is no variability; All the numbers in the data set are the same.
• The data set 12, 12, 12, 12, 12 has a var. of zero (the numbers are identical).The data set 12, 12, 12, 12, 13 has a var. of 0.167; a small change in the numbers equals a very small var.
• The data set 12, 12, 12, 12, 13,013 has a var. of 28171000; a large change in the numbers equals a very large number.
• The formula for sample variance looks like this:

Standard deviation:

• The standard deviation is an outline proportion of the distinctions of every perception from the mean. On the off chance that the distinctions themselves were included, the positive would precisely adjust the negative thus their total would be zero. Thusly the squares of the distinctions are included. The total of the squares is then partitioned by the quantity of perceptions less oneto give the mean of the squares, and the square root is taken to take the estimations back to the units we began with.
• (The division by the quantity of perceptions less oneinstead of the quantity of perceptions itself to acquire the mean square is on the grounds that "degrees of flexibility" must be utilized. In these conditions they are one not as much as the aggregate. The hypothetical avocation for this need not inconvenience the client practically speaking.)
• standard deviation equation :

The standard deviation is given by the equation: s signifies 'standard deviation'. Presently, subtract the mean separately from every one of the numbers given and square the outcome. This is proportionate to the (x - )² step.