Question

Colin and Jezebel are employees at Game Zone. They recorded the number of computer games they sold each week for the past 9 weeks. Colin 15 20 21 9 3 16 9 14 17 Jezebel 10 14 20 11 4 26 5 8 20 (a) All of the games sold of which person had the greatest spread? Explain how you know. (b) The middle 50% of the games sold of which person had the least spread? Explain how you know. (c) What do the answers to Parts 2(a) and 2(b) tell you about Colin's and Jezebel's sold games?

Answer 1

Explanation:

1. a) spread is the range which is given as Max(S)- Min(S)

Colin =

`3,9,9,14,15,16,17,20,21\\\\range=21-3=18\\\\`

Jezebel=

`=4,5,8,10,11,14,20,20,26\\\\range=26-4=22`

Jezebel had a greatest spread.It was 22 while for Colin was 18

2. a) The middle 50% of the game sold is the difference between the third quartile and first quartile of the data

Colin=

`=3,9,9,14,15,16,17,20,21\\\\median=15\\\\lower half=3,9,9,14\\\\\\Q1=(9+9) /2 =9\\\\\\Upper half= 16,17,20,12\\\\\\Q3=(17+20)/2 = 18.5\\`

⇒The middle 50% = Q3-Q1 = 18.5- 9 = 9.5

Jezebel

`=4,5,8,10,11,14,20,20,26\\\\\\=lower half= 4,5,8,10\\\\\\upper half=14,20,20,26\\\\\\Q1=(5+8)/2 = 6.5\\\\Q3= (20+20)/2 = 20`

⇒The middle 50% = Q3-Q1 = 20-6.5 = 13.5

Colin had the least spread of 9.5 as compared to Jezebel who had 13.5

c)The answers in part 2a and 2 b tels us that the middle section that contained 50% of the scores was more in Jezebel record than in Colin records.