Question

Calculate the five-number summary of the given data. Use the approximation method.

13,16,24,18,10,25,24,13,20,18,8,15,18,15,20

Answer 1

Five number summay contains minimum, first quartile, median, third quartile, and maximum of data. Our data is

13,16,24,18,10,25,24,13,20,18,8,15,18,15,20

Let us order this in increasing order

8 10 13 13 15 15 16 18 18 18 20 20 24 24 25

So Minimum = 8 and Maximum = 25.

Length of data is 15. so median is the (15+1)/2 =8th value in sorted data which is 18. so median is 18.

Now to find first and third quartile just take the data below and above the median value and find its median.

Data below median is 8 10 13 13 15 15 16, whose length is 7 so (7+1)/2 = 4th value is median. Thus first quartile of data is 13.

Simillarly data above median is 18 18 20 20 24 24 25, whose length is 7 so (7+1)/2 = 4th value is median. Thus third quartile of data is 20. So five number summary is

    Min.  1st Qu.  Median   3rd Qu.    Max. 
   8.00   13.00    18.00    20.00     25.00