Let's test choice A.
The 13- to 15-year olds spent an average of 14 hours studying last week.
(6 + 7 + 8 + 10 + 12 + 12 + 12 + 13 + 14 + 14)/10 = 10.8 = average
The 13- to 15-year olds spent an average of 10.8 hours studying last week. not 14. Thus, Choice A is incorrect.
Let's test Choice B.
The median value for the hours spent studying last week for the 13- to 15-year olds is greater than the median value for the hours spent studying last week for the 16- to 18-year olds.
The median is found by finding the middle number/set in the data given. Observe.
13- to 15-year olds: 6, 7, 8, 10, (12, 12,) 12, 13, 14, 14
12 + 12 = 24/2 = 12
Median: 12
16- to 18-year olds: 3, 8, 9, 9, (9, 10,) 13, 14, 15, 18
9 + 10 = 19/ 2 = 9.5
Median: 9.5
Therefore, Choice B is true since the median value for the hours spent studying last week for the 13- to 15-year olds is greater than the median value for the hours spent studying last week for the 16- to 18-year olds.
As for Choices C and D, they are incorrect. C is incorrect because the range of the 13- to 15-year olds is 14 - 6 = 8 and the range of the 16- to 18-year olds is 18 - 3 = 15. So this means, The range for the hours spent studying last week for the 13- to 15-year olds is NOT the same as the range for the hours spent studying last week for the 16- to 18-year olds. Thus, C is incorrect.
D is incorrect because the mode for the 16- to 18-year olds is 9 and the mode for the 13- to 15-year olds 12. Thus, the mode for the hours spent studying last week for the 13- to 15-year olds is NOT less than the mode for the hours spent studying last week for the 16- to 18-year olds. Therefore, D is incorrect.
In conclusion, Choice B is the correct answer.
Happy Studying!