Question

3) In the data from the first problem, one of the scores of a winning team was 131 points. Use what you learned in CH. 3-2, plus the calculated mean and standard deviation, to answer the following question: Is 131 points an unusual score for this group of data? Why or why not? Support your answer by telling me what you did to come to your conclusion. Calculated MEAN (round to the nearest whole number):

FREQUENCY DISTRIBUTION TABLE

CLASSES	FREQUENCIES f
75-83	4
84-92	6
93-101	7
102-110	7
111-119	3
120-128	1
129-137	2
138-146	0
147-155	0

Answer 1

CLASSES	FREQUENCIES(f)	Midpoint (x)	f*x
75-83	4	79	316
84-92	6	88	528
93-101	7	97	679
102-110	7	106	742
111-119	3	115	345
120-128	1	124	124
129-137	2	133	266
138-146	0	142	0
147-155	0	151	0

Mean = SUM(f*x) / SUM(f)

Mean = 3000/30 = 100

CLASSES	FREQUENCIES(f)	Midpoint (x)	f*x	f*(x -Mean)^2
75-83	4	79	316	1764
84-92	6	88	528	864
93-101	7	97	679	63
102-110	7	106	742	252
111-119	3	115	345	675
120-128	1	124	124	576
129-137	2	133	266	2178
138-146	0	142	0	0
147-155	0	151	0	0

Considering the Data given is coming from population, then variance

Variance = SUM(f*(x -Mean)^2) / SUM(f) = 6372/30 = 212.4

Standard deviation = = 4.57

Now Mean + 3 * SD = 143.721

Since 131 is lower than (Mean + 3 * SD), it doesn't look unusual. It is within upper control limit.