SEMI-INTERQUARTILE RANGE

The difference between the highest and lowest observation could also be characterized as the range. The range of observation is the term used to describe the outcome. In statistics, the range denotes the dispersion of observations. The difference between the largest value and the smallest values in a set of data is known as the range in statistics. The difference here is that the range of a collection of data is calculated by subtracting the sample maximum and minimum values.

DISPERSION: –

The state of being distributed or spread is known as dispersion. The extent to which numerical data is likely to vary around an average value is referred to as statistical dispersion. In other words, dispersion aids in the comprehension of data distribution.

The measure of dispersion:-

Measures of dispersion are used in statistics to interpret data variability, i.e. to determine how homogeneous or heterogeneous the data is. In simple words, it indicates whether the variable is squeezed or distributed.

Generally, there are two methods by which we can measure the dispersion of the data i.e.

• The Absolute measure of dispersion
• The relative measure of dispersion

The absolute measure of dispersion:-

An absolute measure of dispersion consists of the same unit as the original data set is used in an absolute measure of dispersion. The absolute dispersion approach expresses changes as the average of observed deviations, such as standard or means deviations. It includes terms such as range, standard deviation, and quartile deviation, among others.

Some of the types of absolute measures of dispersion are:-

1. Range:- The difference between the highest and lowest observation could also be characterized as the range. The range of observation is the term used to describe the outcome.
2. Variance:– The variance is calculated by subtracting the mean from each data point in the set, then squaring and adding each square, and lastly dividing them by the total number of values in the data set.
3. Standard deviation:- the square root of the variance is known as standard deviation.
4. Mean and mean deviation:- The mean is the arithmetic mean of the absolute deviations of the observations from a measure of central tendency, and the mean deviation is the arithmetic mean of the absolute deviations of the data from a measure of central tendency (also called mean absolute deviation).

Relative measure of dispersion

When comparing the distribution of two or more data sets, relative measures of dispersion are used. This metric compares values without the use of units. The following are some examples of common relative dispersion methods:

1. Coefficient of Range
2. Coefficient of Variation
3. Coefficient of Standard Deviation
4. Coefficient of Quartile Deviation
5. Coefficient of Mean Deviation

QUARTILE RANGE:-

The quartiles are the values in a piece of data that divide it into four equal portions. A set of data is divided in half by its median.

The lower quartile (LQ) or Q1 is the median of the lower half of a set of data.

The upper quartile (UQ) or Q3 is the median of the upper half of a set of data.

The interquartile range is a measure of variation that is calculated using the upper and lower quartiles.

The interquartile range, or IQR, is the range of a collection of data in the middle half. It refers to the disparity between the upper and lower quartiles.

Q3-Q1 is the interquartile range.

SEMI-INTERQUARTILE RANGE:-

The semi-interquartile range (SIR) is a measure of spread (also known as the quartile deviation). It provides information about how data is distributed around a central point (usually the mean). Half of the difference between the first and third quartiles is the semi-interquartile range. It takes half the time to cover half of the scores. Extreme scores have little impact on the semi-interquartile range. As a result, it’s a useful spread indicator for skewed distributions. It’s calculated by weighing the pros and cons of several options.

Half of the interquartile range is represented by the semi interquartile range.

CALCULATION OF SEMI INTERQUARTILE RANGE:-

The semi interquartile range is calculated by the following steps:-

Step1:– From the given data, write down the first quartile Q1

Step2:-From the given data, write down the third quartile Q3

Step3: – Subtract Q1 from Q2

Step4: – Divide step 3 by 2 then we get the semi quartile range

SEMI QUARTILE RANGE (QUARTILE DEVIATION)=(THIRD QUARTILE (Q3)-FIRST QUARTILE (Q1))/2

QD=1/2(Q3-Q1)

CONCLUSION:-

A distribution’s semi-interquartile range is half of the difference between the upper and lower quartiles, or half of the interquartile range. The semi-interquartile range is a measure of a variable’s dispersion or spread; it is half the distance between the first and third quartiles.