Does the mean or median provide a better summary of data

Assignment Help Basic Statistics

Reference no: EM132393859

Assignment -The scrabble and the mean and median

In the game of Scrabble, letter tiles are placed on a board to form words. Each letter has a point value, with points differing from letter to letter. Players form words with their tiles, a score is given for each word and their total updated after each player has had their turn.

Task 1: Discovering ScrabbleT scoring in the English language

In a ScrabbleTM set there are 100 tiles (including two blank tiles). Below is a table of each letter and the points awarded.

Letter	Number of Tiles	Points
A	9	1
B	2	3
C	2	3
D	4	2
E	12	1
F	2	4
G	3	2
H	2	4
I	9	1
J	1	8
K	1	5
L	4	1
M	2	3
N	6	1
O	8	1
P	2	3
Q	1	10
R	6	1
S	4	1
T	6	1
U	4	1
V	2	4
W	2	4
X	1	8
Y	2	4
Z	1	10
Blank	2

Do you think the same tiles and points will give fair scores in a language other than English? Explain why here.

Task 2: Analysing Scrabble winning margins

A Scrabble' club played 30 games over a one-week period.

Below is a table of the results of these games showing the scores of the losing and the winning player, and the margin (or difference) in their scores.

Game	Losing Score	Winning Score	Margin
1	183	331	148
2	334	400	66
3	215	267	52
4	283	343	60
5	365	444	79
6	225	288	63
7	180	393	213
8	302	372	70
9	343	413	70
10	367	450	83
11	293	370	77
12	270	340	70
13	324	397	73
14	374	435	61
15	300	386	86
16	301	375	74
17	71	296	225
18	318	394	76
19	387	449	62
20	215	303	88
21	189	262	73
22	326	386	60
23	216	277	61
24	212	262	50
25	153	228	75
26	234	317	83
27	38	227	189
28	301	383	82
29	354	411	57
30	235	319	84

Does the mean or median provide a better summary of the data? State which measure is the better statistic in this case and explain how you know that it is a better value to use.

Task 3: Analysing the English-language version of Scrabble

Find a sample of 50-100 words of typical English-language text from a written source (e.g. newspaper, book, magazine, website).

Find a second sample of 350-400 words from a different source.

For each sample:

1. count the number of times each letter appears in each text sample (this can be done manually or electronically)

2. show all results in appropriate tables

3. find the proportions (as percentages) of each letter in each of the texts

4. graph the results of each sample on the same set of axes.

Which sample is more representative of letter distribution in the English language? Justify your reasons and mathematical thinking.

Task 4: Developing Scrabble in another language

Now its time to collect your evidence using a language other than English to help you answer the question:

How might Scrabble scoring work in another language?

• Collect data from an appropriate text source in another language.

• Decide how many tiles there will be of each letter.

• Decide the value of each tile.

Reference no: EM132393859

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