Cumulative Frequency...HELP (1 Viewer)

[rebecca9]

I know this is pretty lame and i should know this stuff, but im studying for trials using past HSC papers and im really stuck on Cumulative Frequency Graph Displays.
im using the 2001 general maths paper and if you care to look its question 25 part b.
ive been looking at the notes from the markers to see if im in the right direction and they say the way i interpret the graph is wrong (apparently). so if someone could have a look at the exam and give me an answer with a reason that would be great. heres the link:

http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2001exams/pdf_doc/gen_mathemat_01.pdf

Thanks heaps

bec.

 

[bored of sc]

(i) 42 - 26 = 16
(ii) 78kg --> anything in the 70-79kg range would probably be correct
(iii) 16 x (300/50) = 96
(iv) 1) The conditions used for the survey were pre-determined and controlled by Armand completely.
2) Selecting 50 students throughout the course of a school day without paying attention to time nor order.

 

[bored of sc]

(i) 42 - 26 = 16
With this (and for any) cumulative frequency graph, as you move to the right across the x-axis (the weight) you gain all the number of students of the preceding weights. For this question, there are 42 students that weigh 80-89kg OR LESS. There are 26 students who weigh 70-79kg OR LESS. Therefore, if you subtract the number of students that weigh 80-89 or less (42) from the number of students that weigh 70-79 or less (26) you get the number of students who weigh 80-89 kg (16).

(ii) 78kg --> anything in the 70-79kg range would probably be correct.
The median means the middle. Since there a 50 students in the sample the middle is 25. So from the graph, go to 25 on the y-axis and read horizontally across till you reach the OGIVE (the straight line going through the bars of the graph). From the Ogive you reached, read of the respective x-axis value. In this case, it lies within the 70-79kg range, and from the ogive I estimated approximately 78kg.

(iii) 16 x (300/50) = 96
Find out the number of students who weighed less than 70kg in the sample of 50 (turns out to be 16, remember NOT to include the 70-79kg range).
If 50 students were sampled and there are 300 in Armand's grade to get an expectation of all 300, multiply by (number of students in grade/number of students surveyed) which turns out to be 300/50 = 6.
So to get the answer go number of students who weighed less than 70kg in the sample of 50 multiplied by (number of students in grade/number of students surveyed) = 16 x (300/50) = 16 x 6 = 96 students.

(iv) 1) The conditions used for the survey were pre-determined and controlled by Armand completely.
2) Selecting 50 students throughout the course of a school day without paying attention to time nor order.

I wasn't too sure about these last two answers.

 

[rebecca9]

cheers. thanks heaps