Consider the following stem-and-leaf display. Stem Leaf 3 1356 4 0013578 5 11256
ID: 2944380 • Letter: C
Question
Consider the following stem-and-leaf display.Stem Leaf
3 1356
4 0013578
5 112569
6
7 01468
8 477
9 03
A. Write down the raw data displayed by thestem-and-leaf display.
B. Obtain the five-number summary (i.e. Min, Q1,Q2, Q3, Max) for the given Data.
C. Construct a box plot using the statistics computed in partb.
I have the ANSWERbut I need to know how do you get this. Please show all steps, Willgive a Lifesaver, Thank You
31,33,35,36,40,40,41,43,45,47,48,51,51,52,55,56,59,70,71,74,76,78,
84,87,87,90,93
MIN=31,Q1=41, Q2=52, Q3=76,MAX=93
Explanation / Answer
(A)The stem and leaf plot is developed by first determining the stemand then adding leaves. With respect to the data, the stem isformed by the "tens" digit and the leaves are the "ones" digit. Thefirst raw data is stem "3" plus leaf "1" and we get the first rawdata , 31. The second raw data is stem "3" plus leaf "3" and we getthe second raw data , 33... Some raw data values may reappear, suchas in the stem "4". So, we have two leaves of "0" in stem "4", i.e.40 and 40... (B)Total number of raw data is n = 27. So, location of Q2 =(n + 1) / 2 = 14. Then Q2 = 52. The first quartile Q1 is the median of the observationswhose position in the ordered list is to the left of the locationof the overall median (i.e. n = 13 now). So, location ofQ1 = (13 + 1) / 2 = 7. Then Q1 = 41. The third quartile Q3 is the median of the observationswhose position in the ordered list is to the right of the locationof the overall median . So, location of Q3 = (thelocation of Q2) + [(n + 1) / 2] = 14 + (13 + 1) / 2 =21. Then Q3 = 76.