IQR

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q1 and the third quartile is denoted as Q3 . Therefore, quartile deviation is not affected by the extreme values of the series.

Range takes only the maximum and minimum values into account and not all the values. Hence it is a very unstable or unreliable indicator of the amount of deviation. It is affected by extreme values.

Arithmetic mean

An extreme value, or extremum (plural extrema), is the smallest (minimum) or largest (maximum) value of a function, either in an arbitrarily small neighborhood of a point in the function’s domain — in which case it is called a relative or local extremum — or on a given set contained in the domain (perhaps all of it) — …

It is not much affected by extreme values. For calculating mean deviation, deviations can be taken from any average.

An extreme value can affect the value of the median only if it is really large. An extreme value will not affect the value of the median any more than other values. Extreme values can influence the median in the same way as the mean. No values, extreme or otherwise, can affect the value of the median.

Median is the value that divides the data set in exactly two parts. One of the advantages of median is that it is not effected by the outliers.

The mode is easy to understand and calculate. The mode is not affected by extreme values. The mode is easy to identify in a data set and in a discrete frequency distribution. The mode is useful for qualitative data.

The mean is sensitive to all scores in a sample (every number in the data affects the mean), which makes it a more “powerful” measure than the median or mode. The mean’s sensitivity to all scores also makes it sensitive to extreme values, which is why the median is used when there are extreme values.

Definition Extreme value These characteristic values are the smallest (minimum value) or largest (maximum value), and are known as extreme values. For example, the body size of the smallest and tallest people would represent the extreme values for the height characteristic of people.

Explanation: To find extreme values of a function f , set f'(x)=0 and solve. This gives you the x-coordinates of the extreme values/ local maxs and mins.

Find the first derivative of f using the power rule. Set the derivative equal to zero and solve for x….Here’s how:

1. Take a number line and put down the critical numbers you have found: 0, –2, and 2.
2. Pick a value from each region, plug it into the first derivative, and note whether your result is positive or negative.

Use basic rules of algebra to rearrange the function and solve the value for x, when the derivative equals zero. This solution will tell you the x-coordinate of the vertex of the function, which is where the maximum or minimum will occur. into the original function and solve to find the minimum or maximum.

Important: Although a function can have only one absolute minimum value and only one absolute maximum value (in a specified closed interval), it can have more than one location (x values) or points (ordered pairs) where these values occur.

If the derivative of a function changes sign around a critical point, the function is said to have a local (relative) extremum at that point. Also, f'(x) changes from positive to negative around 0, and hence, f has a local maximum at (0,0). …

So there is no overall maximum: there can be as many inflection points as you like between two adjacent critical points. If you want an answer in terms of the degree of the polynomial, the maximum is the degree minus 2.