Mrs. Juarez graded ten English papers and recorded the scores.

92, 95, 100, 62, 88, 90, 100, 96, 89, 98

Which statements are true? Check all that apply.
The range of scores is 38.
Without the outlier, the range of scores would be 12.
The outlier impacts the range more than it impacts the interquartile range.
The interquartile range is 9.
The interquartile range is 4.
Without the outlier, the interquartile range would be 9.5.

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.