Which of the following options is a better purchase for a bicycle? option 1: a cash sale for $88 option 2: $5 down with equal payments of $8 for 10 weeks option 3: $12 down with equal payments of $5 for 12 months option 4: $20 down with equal payments of $20 for 12 months

Table of ordered data

number of       value
data

1                      62
2                      88
3                      89
4                      90
5                      92
6                      95
7                      96
8                      98
9                    100
10                  100

Range of scores: 100 - 62 = 38

Oulier: 62 => Range without the outlier = 100 - 88 = 12

Interquartile range, IQR, = difference between third quartile and first quartile: IQR = Q3 - Q1

Quartlies of all the data:

1                      62
2                      88
3                      89   first quartile, Q1 = 89
4                      90
5                      92
median, Q2 = (95 + 92) / 2 = 93.5
6                      95
7                      96
8                      98 third quartile, Q3 = 98
9                    100
10                  100

=> IQR = 98 - 89 = 9 : the interquartle range is 9

Quartlies without the outlier:

2                      88
3                      89
first quartile, Q1 = (89 + 90) / 2 = 89.5
4                      90
5                      92
6                      95 median, Q2 = 95
7                      96
8                      98
third quartile, Q3 = (98 + 100) / 2 = 99
9                    100
10                  100

=> IQR = Q3 - Q1 = 99 - 89.5 =  : the interquartle range without the outlier is 9.5

Therefore, the outlier impacts more the range than it impacts the IQR.

THE ONLY STATEMENT THAT IS FALSE IS THE NUMBER 5.