Date | May 2019 | Marks available | 2 | Reference code | 19M.1.SL.TZ2.S_8 |
Level | Standard Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 2 |
Command term | Find | Question number | S_8 | Adapted from | N/A |
Question
A group of 10 girls recorded the number of hours they spent watching television during a particular week. Their results are summarized in the box-and-whisker plot below.
The group of girls watched a total of 180 hours of television.
A group of 20 boys also recorded the number of hours they spent watching television that same week. Their results are summarized in the table below.
The following week, the group of boys had exams. During this exam week, the boys spent half as much time watching television compared to the previous week.
For this exam week, find
The range of the data is 16. Find the value of .
Find the value of the interquartile range.
Find the mean number of hours that the girls in this group spent watching television that week.
Find the total number of hours the group of boys spent watching television that week.
Find the mean number of hours that all 30 girls and boys spent watching television that week.
the mean number of hours that the group of boys spent watching television.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
valid approach (M1)
eg 16 + 8, − 8
24 (hours) A1 N2
[2 marks]
valid approach (M1)
eg 20 − 15, , 15 − 20
IQR = 5 A1 N2
[2 marks]
correct working (A1)
eg , ,
mean = 18 (hours) A1 N2
[2 marks]
attempt to find total hours for group B (M1)
eg
group B total hours = 420 (seen anywhere) A1 N2
[2 marks]
attempt to find sum for combined group (may be seen in working) (M1)
eg 180 + 420, 600
correct working (A1)
eg ,
mean = 20 (hours) A1 N2
[3 marks]
valid approach to find the new mean (M1)
eg ,
mean (= 10.5) hours A1 N2
[2 marks]