Question 1
High scores are collected for an eSports event held in the city centre.
The range was large so the organisers wanted to have them arranged in a grouped frequency table.
The scores are given below:
Find the missing values of the grouped frequency table below.
ANSWER: Multiple Answers (Type 1)
Answers: a=3, b=2, c=5, d=3, e=6
Workings:
For each class, count up the number of scores from the data provided for that class. Add this to the table.
Marks = 3
Question 2
The following grouped frequency table shows time, in minutes, visitors spent on a popular website over the course of one day.
2(a):
Visitors who spent more than 4 minutes on the website were directed to a survey where they could enter a prize draw after they gave feedback.
How many visitors were directed to the survey?
ANSWER: Simple Text Answer
Answer: 13634
Workings:
Sum the frequencies of the last three classes:
6248 + 4635 + 2751 = 13634
Marks = 1
2(b):
Does this grouped frequency table identify how many visitors spent less than one minute on the website?
ANSWER: Multiple Choice (Type 2):
A: Yes
B: No
Answer: B
Workings:
No, because it’s impossible to tell how many people in the 0 < t \leq 2 category also fit into the 0 < t \leq 1 category, as no specific data is given for this.
Marks = 1
Question 3
A volunteer lost part of the results of a survey that showed the time, t, people planned to spend at the gym, one day.
The volunteer knows that the number of people who spent more than 30 minutes was 84.
What is the missing value in the table?
ANSWER: Simple Text Answer
Answer: 15
Workings:
Adding the two values given in the 30 < t \leq 75 range gives 27 + 42 = 69.
The total for this range is 84, so the missing value can be calculated as
84 - 69 = 15
Marks = 2
Question 4
In a biology class, students recorded heights of plants, after caring for them over a 2 month period.
Two plant heights were not recorded; both were the same height.
If they had been added, their category would become the second most common.
Which category did the two plants belong to?
ANSWER: Multiple Choice (Type 2)
A: 0 < h \leq 10
B: 10 < h \leq 20
C: 20< h \leq 30
D: 30 < h \leq 40
Answer: B
Workings:
Looking through the classes, 10 < h \leq 20 is the only class where an addition of 2 would change its position in the rankings by frequency.
It is originally the third placed class with 11, but adding 2 would increase it to 13, making it the second placed class.
Marks = 2
Question 5
The times for goals scored by a local football team are recorded in the following table. Extra time goals are not included.
5(a):
Which class contains the median from this grouped frequency table?
ANSWER: Multiple Choice (Type 2)
A: 15 < t \leq 30
B: 60 < t \leq 75
C: 30 < t \leq 45
D: 45 < t \leq 60
Answer: D
Workings:
\dfrac{n+1}{2} = \dfrac{80+1}{2} = 40.5
The 40^{th} and 41^{st} values both lie in the 45 < t \leq 60 class, so this is the median class.
Marks = 1
5(b):
Find the modal class of this grouped frequency table.
ANSWER: Multiple Choice (Type 2)
A: 15 < t \leq 30
B: 60 < t \leq 75
C: 30 < t \leq 45
D: 75 < t \leq 90
Answer: D
Workings:
The modal class is the most frequently occurring one, which is 75 < t \leq 90
Marks = 1
Question 6
Data on the time taken for 90 students to complete a 200m race has been summarised in the grouped frequency table below.
6(a):
Why is the mode an inappropriate measure of the average in this case?
ANSWER: Multiple Choice (Type 1)
A: The groups are similar in size
B: There are too many results
C: The results are not big enough
D: The results vary too much
Answer: A
Workings:
The groups are all similar size, which makes it more difficult to suggest one class is more frequent on than the others.
Marks = 1
6(b):
Which of the following could be used as an improvement to the grouped frequency table?
ANSWER: Multiple Choice (Type 1)
A: Split each group into smaller groups.
B: Merge some of the groups together.
C: Use a smaller sample.
D: Make everyone run a longer race.
Answer: A
Workings:
Splitting the groups up into 0.5 seconds groups could give a better view of how students did the race.
Marks = 1
Question 7
Ben and Jane both collected data on the English marks for two year 9 classes.
Their data has been summarised below
7(a):
Combine Ben and Jane’s data in a single grouped frequency table shown below.
ANSWER: Multiple Answers (Type 1)
Answers: a = 10, b = 16, c = 26, d = 12, e = 6
Workings:
Work out which groups in each of Ben and Jane’s tables corresponds to the combined group and sum together.
a = 1 + 4 + 5 = 10
b = 12 + 3 + 1 = 16
c = 15 + 11 = 26
d = 6 + 6 = 12
3 = 2 + 4 = 6
Marks = 3
7(b):
What is one advantage of combining the results into one grouped frequency table?
ANSWER: Multiple Choice (Type 1)
A: Only need to calculate one mean
B: Less data to look at
C: Less group classes
D: Can compare the classes
Answer: A
Workings:
If two separate classes are used, it would be necessary to calculate the mean of each group separately and then compare.
By combining the tables together, it is possible to calculate just one mean for the entire data set.
Marks = 2
Question 8
Times for racing snails to complete a course were recorded.
The grouped frequency table displays their results.
8(a):
What is the total number of snails that took longer than 100 seconds but no more than 400 seconds to complete the course?
ANSWER: Simple Text Answer
Answer: 30
Workings:
The question can be represented as an inequality, 100 < s \leq 400.
This covers the group classes 100 < s \leq 200, 200 < s \leq 300, 300 < s \leq 400.
Summing their frequencies together gives:
6 + 8 + 16 = 30
Marks = 1
8(b):
In which category will you find the median of the value given in part (a)?
ANSWER: Multiple Choice (Type 2)
A: 100 < s \leq 200
B: 200 < s \leq 300
C: 300 < s \leq 400
D: 400 < s \leq 500
Answer: C
Workings:
\dfrac{n+1}{2} = \dfrac{30+1}{2} = \dfrac{31}{2} = 15.5
The 15^{th} and 16^{th} values both fall in the 300 < s \leq 400 group, which gives the median.
Marks = 1
8(c):
Find the modal class of this grouped frequency data.
ANSWER: Multiple Choice (Type 2)
A: 100 < s \leq 200
B: 200 < s \leq 300
C: 300 < s \leq 400
D: 400 < s \leq 500
Answer: C
Workings:
Of the group classes being used, 300 < s \leq 400 has the highest frequency, so it is the modal class.
Marks = 1