Five Number Summary Boxplots and Outliers Statistics Exercises

the five number summary of data set consists of the minimum the first quartile the median the third quartile and the maximum with the five number summary you can then construct box plot to represent the data set to find the five number summary of this data set we should begin by putting it in order from least to greatest and that gets us here we see the minimum is zero the maximum is 10. the median is the number in the middle or in this case because we have an even data set it's the average of the two numbers in the middle so that's just three plus four divided by two you can also just think of this as the number that's halfway between the two numbers in the middle if we had one more number in this data set the median would just be the number in the middle in this case that would have been four so we found the minimum the maximum and we just found the median is 3.5 to find the first and third quartiles we need to split the data in half just like that we have our lower half of data the median of that is q1 and the upper half of data the median of that is Q3 we see the median of the lower half of data is 2 so that's q1 the median of the upper half of data is 5 so that's Q3 to use the five number summary to construct box plot we need number line that goes from our minimum zero to our maximum 10. there's our number line then we just draw vertical lines for all the numbers in the five number summary the minimum the maximum and the quartiles and median we draw box between q1 and Q3 with the median in the middle the distance between these values or the width of the box is the interquartile range and then we draw what are called whiskers going out to the maximum and the minimum and that's how you make box plot we can also label the value specifically if we need to be extra clear you may also want to consider modified box plot where we can use our intra quartile range the distance between q1 and Q3 to find outliers which we represent differently in modified box plot we see that our maximum of 10 is pretty far from the rest of the data and we can determine if it's an outlier using this rule of thumb value is an outlier if it's less than q1 minus 1.5 times the IQR or greater than Q3 plus 1.5 times the IQR the IQR in our case Q3 minus q1 is 3. once we run the calculations we get lower fence of negative 2.5 and none of our data is below that so there are no lower outliers but our upper fence is 9.5 so we see 10 is indeed an upper outlier to represent that on our box plot we can make it so the maximum whisker only goes to the maximum excluding 10 and then we can just draw DOT to represent 10 as an outlier and that's what this would look like as modified box plot but again you can also just use normal box plot thanks for watching and let me know in the comments if you have any questions check the description for links to related videos for extra practice