Question

The number of total rushing yards for 23 football players for the 2014 and 2015 seasons are listed below.


2014 Total Yards 2015 Total Yards
37 11
76 56
4 4
5 3
50 87
1 2
45 31
82 55
21 3
2 1
35 34
17 22
50 25
8 42
146 147
4 1
51 25
4 5
1 17
23 4
14 10
9 3
42 67

Part A: On your own paper, create a back-to-back stemplot. Submit a list of the stems you used in order from least to greatest. Justify your reasoning for split or nonsplit stems. (4 points)
Part B: Compare and contrast the two data sets. Justify your answer using key features of the data. (6 points)

Answer 1

Answer:

the totalyatds of 2015 is76 56

Answer 2

A stem and leaf plot presents quantitative data graphically

The given data is presented as follows;

$\begin{array}{ccc}2014 \ Total \ Yards&&2015 \ Total \ Yards\\37&&11\\76&&56\\4&&4\\5&&3\\50&&87\\1&&2\\45&&31\\82&&55\\21&&3\\2&&1\\35&&34\\17&&22\\50&&25\\17&&22\\50&&25\\8&&42\\146&&147\\4&&1\\51&&25\\4&&5\\1&&17\\23&&4\\14&&10\\9&&3\\42&&67\end{array}$

Part A

The back to back stem plot is presented as follows;

$\begin{array}{r|c|l}2014 \ Total \ Yards&&2015 \ Total \ Yards\\9 \ 8 \ 5 \ 4 \ 4 \ 4 \ 2 \ 1 \ 1&0&1 \ 1 \ 2 \ 3 \ 3 \ 3 \ 4 \ 4 \ 5\\7 \ 4&1&0 \ 1 \ 7\\3 \ 1 &2&2 \ 5 \ 5\\7 \ 5&3&1 \ 4\\5 \ 2&4&2\\1 \ 0 \ 0&5&5 \ 6\\&6&7\\6&7&\\2&8&7\\6&14&7\end{array}$

The list of stem used which is non split stem is; 0, 1, 2, 3, 4, 5, 6, 7, 8, and 14

This is so because, the values of the data are spread across the tens unit position from 1 to 8

Part B;

The similarities are;

• Both dataset are skewed towards the lower (unit) total yards values

• The number of players that have a unit total yards in 2014 and 2015 are equal to 9

• The number of players in 30s, 80s and 140s are equal in 2014 an 2015

The differences are;

The number of players in the 10s, 20s and 60s are more in 2015 than in 2014, while those 50s and 70s are more in 2014 than in2015

From the data sets, we have that the sum of the total rushing yards for 2014 (727) is more than the sum of the total rushing yards for 2015 (655)

The average for 2014 (31.6087), is therefore, larger for 2014 than 2015 (28.4783)

The standard deviation which is a measure of dispersion is smaller for 2014 (33.9434) is lesser than the standard deviation for 2015 (34.5088)

The median for 2014 (21) is larger than the median for 2015 (17)

Learn more about stem and leaf plot here:

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