A five-number summary is especially useful in descriptive analyses or during the preliminary investigation of a large data set. A summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median.
A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.
The data is arranged in the increasing order. The minimum value in this number is 0 while the maximum number is 11. Thus, the five number summary for the data set 0,2,2,4,5,5,5,5,7,11 is as minimum value is 0, maximum value is 11, median is 5, first quartile is 2 and second quartile is 5.
The IQR can help to determine potential outliers. A value is suspected to be a potential outlier if it is less than (1.5)(IQR) below the first quartile or more than (1.5)(IQR) above the third quartile. Potential outliers always require further investigation.
To calculate the five number summary in Excel: arrange your data in one column; use =MIN(A:A) for the minimum value, =QUARTILE. INC(A:A, 1) for Q1, =MEDIAN(A:A) for the median, =QUARTILE. INC(A:A, 3) for Q3, and =MAX(A:A) for the maximum value. Replace 'A:A' with the actual range of your data.
Five-number summaries
A five-number summary is especially useful in descriptive analyses or during the preliminary investigation of a large data set. A summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median.
The range is the difference between the biggest and the smallest number. To find the range, subtract the lowest number from the biggest number.
The median is the number in the middle of 2, 3, 11, 13, 26, 34, 47 which is 13 in this case because there are three numbers on either side. Determine the middle pair, add them, and divide by two to find the median value in a list with an even amount of numbers.
5-point summary or 5-number summary refers to the 5 important points(or numbers) shown by a box plot. The 5 points refer to the minimum value, 1st quartile, median, 3rd quartile and the maximum value. IQR is defined as the difference between 1st quartile and 3rd quartile. Here, 1st quartile=36 & 3rd quartile=57.
Analyzing skewness based on five-number summary
The skewness of a distribution is determined by comparing the distance of Q1, median, and Q3 from the minimum and maximum respectively. If the median is closer to Q1 than Q3, the distribution is right-skewed. If it's closer to Q3, it is left-skewed.
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