Given the word problem, we can deduce the following information:
1. The dot plots represent the cost of first-year college tuitions for two different U.S. regions.
We can determine the means of the tuition costs of each region by dividing the sum of each set of tuition costs by the number of tuition costs. Base on the given plot dots, the number of tuition costs is 27.
The sets are shown below:
Region 1 ( in thousands)
2,4,5,5,6,6,7,10,13,15,16,17,17,17,19,19,21,22,24,27,27,28,28,31,33,34,37
Sum=490
Region 2(( in thousands)
2,3,3,4,5,5,6,6,7,8,8,8,9,9,9,9,10,10,10,13,15,16,21,22,24,31,37
Sum=310
So, the mean for region 1 is:
Mean = 490/27=18.481
If we convert this into thousands, it would be 18.481x1000=$18481
The mean for regions 2 is:
Mean= 310/27=11.481=$11,481
So, region 1 has greater mean than region 2, and I is true.
The median is the middle of each set data, so the medians of the tuition costs for regions 1 and 2 are $17,000 and $9,000 respectively. Therefore, region 1 has a greater median than region 2, and II is false.
To find the interquartile range, we first determine the first and third quartiles of each data set. The intequartiles for the two regions are shown below:
Region 1:
Interquartile Range =Q3-Q1= 27-7= 20
Region 2:
Interquarile Range = Q3-Q1=15-6=9
So, the interquartile ranges