Middle value or Median can be called as Second Quartile (Q2) and gained by taking the Middle most value after sorting the data
Mode | Mostly appeared
Mode:
The mode is the value that appears most frequently. Here, the mode is the value that most appeared
Q1 | 1st Quartile :
firstQuartile:
The first quartile (25th percentile) is the median of the first half of the sorted data. It's gained by Identify the median of the first half of the sorted data (excluding the overall median if the number of data points is odd).
Q3 | 3rd Quartile :
Third Quartile:
The 75th percentile of the data. It separates the lowest 75% of the data from the highest 25%. Its gained by Identify the median of the second half of the sorted data (excluding the overall median if the number of data points is odd).
Q3 | 4th Quartile there
Fourth Quartile
... .....
IQR | Inter Quartile :
Inter Quartile:
The Its gained by Subtracting Q1 from Q3. (Q3 - Q1)More about IQR:
Usage Measure of Spread:
The IQR provides a measure of the spread of the middle 50% of the data, giving a sense of the variability without being affected by extreme values.
Identifying Outliers:
Outliers can be identified using the IQR. Typically, an outlier is any data point that is more than 1.5 times the IQR above Q3 or below Q1.
Lower Bound=Q1−1.5×IQR Upper Bound =Q3+1.5×IQR Example of Identifying Outliers
For the given data set: [0,0,0,0,1,2,3,4,5,8,67,1000]
Lower Bound: 0−1.5×37.5=−56.25
Upper Bound: 37.5+1.5×37.5=93.75
Any data point below -56.25 or above 93.75 is considered an outlier. In this case, 1000 is an outlier.
Robustness:
The IQR is a robust measure of variability because it is not influenced by outliers or extreme values, unlike the range or standard deviation.
Conclusion
The IQR is a valuable statistical tool used to understand the spread and central tendency of a data set, as well as to identify outliers.
It provides a clear picture of the middle 50% of the data, making it useful for robust statistical analysis.
Special Case (byof)| Number Involved in there
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