Amanda surveyed 20 juniors and seniors at Delmark Highschool to find the number of hours per week they spend working at part time jobs. Her results are shown below
Junior - 20,10,20,15,0,0,10,20,15
Senior - 20,20,10,10,0,0,0,10,0,10
Which statement about the data is true?
A - The range of hours worked is the same for juniors and seniors.
B - The mean , median, and mode for the juniors surveyed fall within 3-hour range.
C - The mean number of hours worked by the seniors surveyed is 12.
D - The mean number of hours worked is the same for juniors and seniors.
I think it is A because the range for both juniors and seniors is 20. I also think it is B.
-Please help thank you!
Yes, A.
think not on B.
So, is it A?
To answer this question, let's analyze each statement and determine if it is true or false:
Statement A: The range of hours worked is the same for juniors and seniors.
To find the range, we subtract the smallest value from the largest value in each group.
For juniors: Range = 20 - 0 = 20
For seniors: Range = 20 - 0 = 20
Since both juniors and seniors have a range of 20, Statement A is true.
Statement B: The mean, median, and mode for the juniors surveyed fall within a 3-hour range.
To check this statement, let's find the mean, median, and mode for the juniors surveyed.
Mean = (20 + 10 + 20 + 15 + 0 + 0 + 10 + 20 + 15) / 9 = 110 / 9 = 12.22 (approximately)
To find the median, we need to sort the data in ascending order: 0, 0, 10, 10, 15, 15, 20, 20, 20. The median is 15.
The mode is 20 since it appears more frequently than any other value.
The range within the given juniors data is 20 - 0 = 20.
Since the mean, median, and mode are not within a 3-hour range, Statement B is false.
Statement C: The mean number of hours worked by the seniors surveyed is 12.
To find the mean for the seniors, we sum up the values and divide by the number of values.
Mean = (20 + 20 + 10 + 10 + 0 + 0 + 0 + 10 + 0 + 10) / 10 = 90 / 10 = 9.
Since the mean is 9, Statement C is false.
Statement D: The mean number of hours worked is the same for juniors and seniors.
We have already calculated the mean for juniors as 12.22 and for seniors as 9. Therefore, the mean number of hours worked is different for juniors and seniors. So, Statement D is false.
In conclusion, the correct statements are A (the range is the same for juniors and seniors) and B (the mean, median, and mode for the juniors do not fall within a 3-hour range).