Part A – Statistical Investigation with Manual Calculations
Match
No. | Season | |
2021 | 2022 | |
1 | 51 | 86 |
2 | 50 | 16 |
3 | 25 | 40 |
4 | 14 | 32 |
5 | 13 | 26 |
6 | 12 | 24 |
7 | 11 | 20 |
8 | 11 | 19 |
9 | 11 | 17 |
10 | 7 | 14 |
11 | 7 | 9 |
12 | 6 | 3 |
13 | 3 | 6 |
14 | 15 | 7 |
15 | 25 | 5 |
16 | 10 | 52 |
17 | 9 | 13 |
18 | 61 | 24 |
19 | 51 | 41 |
20 | 37 | 22 |
21 | 35 | 12 |
22 | 13 | 10 |
23 | 8 | 16 |
24 | 0 | 25 |
25 | 45 | 75 |
The Sydney Sixers Cricket Team has a history of success since the league’s inception in 2011, but lost the Big Bash final in 2022. Daniel Hughes is a Batsmen for the Sixers is considered one of the team’s leading run scorers.
At the end of the 2022 season, the coach approached Daniel Hughes and suggested that the Sixers may need to trade him to another team. The reason given by the coach is that overall, Hughes’ scoring was not as good in the 2022 season as it was in 2021.
Daniel is unsure of the coach’s suggestion and he obtained a list of his data for both the 2021 and 2022 seasons. This table shows the number of runs he scored per match, in each of the 25 matches he played, in both seasons.
(For example, in Match 12 of the 2021 season, he scored 6 points)
Daniel’s problem is that he doesn’t remember any of his high school mathematics, so he is unsure how the data can help him build a case to argue the coach’s decision.
Your task is to analyse this data to determine whether or not Daniel Hughes can convince his coach that he has reached an incorrect conclusion.
You are to compare and contrast the two sets of data and draw conclusions so that these can be passed on as professional advice to Daniel – his career may depend upon it!
To achieve this, you should:
1. Calculate, using correct formulas and showing substitutions, the following statistical measures:
Central tendency: mean, median, mode
Spread: range, interquartile range
2. Using
Excel, display the data in:
- a histogram
- a back-to-back stem plot
- a parallel box plot (aka box-and-whisker plot), showing the scores in the two seasons on the same set of axes
3. Write a short report that:
- Discusses the data in terms of achievement (scoring output) as well as consistency for each of the two seasons, looking for similarities and differences.
- Draw conclusions and gives a recommendation that Daniel
- can use when he meets with his coach to discuss the situation
- Make specific references to any statistical values calculated, as well as specifying the meaning of that statistic. (eg. his mean score for the 20.. season was …indicating that his average scoring had…. , etc…)