Compare Data Sets
Boys' Lunchboxes Girls' Lunchboxes
4 2
4 3
6 4
7 4
8 5
9 5
9 6
10 7
12 8
The table represents the number of cheese crackers in the lunchboxes of 9 boys and 9 girls. By looking at the table, does it appear that the degree of variability for the boys' data is greater, less, or the same as the girls' data? Compute the interquartile range of each data set. Using the interquartile range, compare the degree of variability between the data sets. Explain how the comparison supports your first answer.
Responses
A no; Boys: IQR: 4.5; Girls IQR: 3; The degree of variability for both sets is about the same.no; Boys: IQR: 4.5; Girls IQR: 3; The degree of variability for both sets is about the same.
B no; Boys: IQR: 3; Girls IQR: 4.5; The degree of variability for both sets is about the same.no; Boys: IQR: 3; Girls IQR: 4.5; The degree of variability for both sets is about the same.
C yes; Boys: IQR: 8; Girls IQR: 5; The degree of variability is greater for the boys than for the girls.yes; Boys: IQR: 8; Girls IQR: 5; The degree of variability is greater for the boys than for the girls.
D yes; Boys: IQR:10; Girls IQR:16; The degree of variability for the boys is less than for the boys.
C yes; Boys: IQR: 8; Girls IQR: 5; The degree of variability is greater for the boys than for the girls.
The interquartile range (IQR) is a measure of variability that describes the range between the 25th and 75th percentiles of a dataset. In this case, the boys' lunchboxes data has an IQR of 8, while the girls' lunchboxes data has an IQR of 5.
Since the IQR for the boys' data is larger than the IQR for the girls' data, it indicates that the range of values in the boys' dataset is greater than that of the girls' dataset. This suggests that the boys' data has a greater degree of variability compared to the girls' data, supporting the initial answer.