Asports club rewards teams based on overall points earned in a season. the data for points are shown in the table, where low represents the fewest points scored and high represents the highest points scored by a single team member. team low high range mean median iqr σ team l 4 17 13 9.4 9 9.75 4.8 team m 6 14 8 9.7 9.5 6.25 3.2 team n 1 20 19 13 14.5 4.75 5.6 part a: if the club wants to award the team that has the most consistent scoring among its team members, which team should it choose and why? justify your answer mathematically. part b: if the club wants to award the team with the highest average score, which team should it choose and why? justify your answer mathematically.

Part A:
For this one, you have to find the median. So first you would put them in order from least to greatest. After you do that you should get,

TEAM L: 4, 4.8, 9, 9.4, 9.75, 13, 17  
TEAM M: 3.2, 6, 6.25, 8, 9.5, 9.7, 14
TEAM N: 1, 4.75, 5.6, 13, 14.5, 19, 20
 next go from side to side crossing them out evenly till you get to the number in the center.
TEAM L: 9.4
TEAM M: 8
TEAM N: 13
the question asks which team scores more consistently so that would be the team with the highest marking which is team n

so your answer for part A is TEAM N would be awarded the team with the most consistent scoring

part B: you find the average by finding the mean. To find the mean you must add all the numbers up and then divide by how many numbers there are. First we are going to add them up,

TEAM L: 4+17+13+9.4+9+9.7+4.8 = 66.95
TEAM M: 6+14+8+9.7+9.5+6.25+3.2 = 56.65
TEAM N: 1+20+19+13+14.5+4.75+5.6 = 77.85

lastly since all of them consist of 7 numbers, you will divide all the solutions by 7 giving you,

TEAM L: 9.56 (rounded)
TEAM M: 8.09 (rounded)
TEAM N: 11.12 (rounded)

the question asks which team has the higher average score, therefore TEAM N would be the answer since it consist of the highest number.

so your answer for part B is TEAM N would be awarded the team with the highest average score.

ANSWERS

PART A: TEAM N would be awarded the team with the most consistent scoring.

PART B: TEAM N would be awarded the team with the highest average score.

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