Question 1
Students in year 7 took an English test. The boys’ results are summarised below.
The lowest mark was 12
The highest mark was 55
The median was 32
The upper quartile was 41
The interquartile range was 22
Which box plot represents this information?
ANSWER: Multiple Choice (Type 2)
A:
B:
C:
D:
Answer: A
Workings:
From the data, the lowest value is 12. There is only one plot that has this as the lowest value.
Marks = 3
Question 2
Students in year 7 took an English test.
The girls’ results are summarised in the table below.
Which box plot displays the above information?
ANSWER: Multiple Choice (Type 2)
A:
B:
C:
D:
Answer: A
Workings:
By finding the lowest and largest values, the upper and lower quartiles and the median, the data can be displayed as a box plot.
Marks = 3
Question 3
Year 8 students took a Maths test.
The summary statistics for both boys and girls are summarised below.
3(a):
Which of the following represents a box plot for the boys’ data?
ANSWER: Multiple Choice (Type 2)
A:
B:
C:
D:
Answer: A
Workings:
Only one box plot has the median line at 55. Therefore, this must be the solution.
Marks = 2
3(b):
Which of the following represents a box plot for the girls’ data?
ANSWER: Multiple Choice (Type 2)
A:
B:
C:
D:
Answer: A
Workings:
There is only one box plot with the median line at 60. Therefore, this must be the solution.
Marks = 2
3(c):
Which of the following is an accurate comparison of the box plots in (b) and (c)?
ANSWER: Multiple Choice (Type 1)
A: The Interquartile ranges are similar.
B: Both have the same lowest value.
C: The median for the boys suggests they scored better than the girls on average.
D: On both plots, the median is exactly half way between the Lower and Upper Quartiles.
Answer: A
Workings:
The IQR for the boys is 70 - 42 = 28.
The IQR for the girls is 72 - 45 = 27
These are very similar results.
Both groups have a different lowest value.
The boys have a lower median than the girls.
The median is half way between the quartiles on neither the boys’ or girls’ box plot.
So the answer must be that the IQR results are similar.
Marks = 2
Question 4
Two classes, 8A and 8B, collect data on the time it takes students to get to school.
This information has been summarised on the box plots below.
4(a):
Find the missing values in the table below.
ANSWER: Multiple Answers (Type 1)
Answer: x = 45, y = 20, z = 55
Workings:
Read off the median line on the axis to find the median for 8B.
Subtract the lower quartile from the upper quartile to find the IQR for 8A.
Subtract the lowest value from the highest value for 8B.
Marks = 3
4(b):
Which class was most consistent overall with the time they took to get to school?
ANSWER: Multiple Choice (Type 1)
A: Class 8A
B: Class 8B
Answer: B
Workings:
The highest value for 8B is closer to its median than in 8A.
The median is half way between the two quartiles in 8B, while in 8A, the median is skewed towards the upper quartile.
This suggests the results in 8B are more consistent.
Marks = 1
Question 5
Two sets of data, A and B, have been plotted as box plots.
5(a):
Which data set has the smallest inter-quartile range?
ANSWER: Multiple Choice (Type 1)
A: Set A
B: Set B
Answer: A
Workings:
The gap between the lower and upper quartiles is much smaller in A than B.
Marks = 1
5(b):
Why is only one characteristic “whisker” shown for data set B?
ANSWER: Multiple Choice (Type 1)
A: The lowest value is the same as the lower quartile.
B: The person collecting the data forgot to put it on.
C: Not enough data was collected.
D: To make the diagram fit the page better.
Answer: A
Workings:
If a whisker appears to be missing from a diagram it implies that the lowest value and lower quartile are the same. This is the same for the highest value and upper quartile.
Marks = 1
5(c):
Which of the following is an accurate comparison between box A and box B?
ANSWER: Multiple Choice (Type 1)
A: Set B has a smaller range & Set A has a smaller IQR
B: Set A has a smaller range & Set B has a smaller IQR
C: Set A‘s highest value was larger than set B‘s
D: Set A has a higher median
Answer: A
Workings:
Although both sets have the same highest value, box B has a bigger lowest value, meaning it will have a smaller range.
The lower quartile and upper quartile are closer together in box A so it has a smaller IQR.
Marks = 2
Question 6
5 friends measure their heights and the results are shown below.
156 cm, 153 cm, 151 cm, 150 cm, 170 cm
A box plot is to be made from this data.
6(a):
Which of the following is a drawback to drawing a box plot for this data?
ANSWER: Multiple Choice (Type 1)
A: Won’t be useful for comparison due to small data set.
B: Doesn’t show the median.
C: Easy to draw due to small data set.
D: Won’t identify any outliers.
Answer: A
Workings:
Because the data set is so small, it will be very difficult to compare it to other data sets as all five values will take one of: the lowest value, lower quartile, median, upper quartile and highest value.
Marks = 1
6(b):
Which of the following is a benefit of using a box plot?
ANSWER: Multiple Choice (Type 1)
A: It is easy to spot outliers.
B: They tell us the mean of the data.
C: Good for comparing small sets of data.
D: They tell us the mode of the data.
Answer: A
Workings:
If either the lowest or highest value is far away from the box part of the diagram, it suggests it is an outlier. In this case it is clearly visible that the highest value, 170 cm, is an outlier.
Marks = 2
Question 7
Tom kept a record of the amount of time Robins spent in his garden at each visit.
The table below shows his summary statistics for the times recorded.
7(a):
Which of the box plots below represents the above data?
ANSWER: Multiple Choice (Type 2)
A:
B:
C:
D:
Answer: A
Workings:
There is only one plot that has a lower quartile of 30 and median of 45. This must be the solution.
Marks = 2
7(b):
Tom logs some extra data about new Robins that have entered his garden.
The new Robins spend the following times in the garden.
20 mins, 25 mins, 27 mins
How will the new data affect the shape of the box plot from part (a)?
ANSWER: Multiple Choice (Type 1)
A: Range unchanged & IQR increased
B: Range increased & IQR increased
C: Range decreased & IQR unchanged
D: Range decreased & IQR decreased
Answer: A
Workings:
None of these values will become a new lowest or highest value, so the range remains unchanged.
Because these values all fall below the previous lower quartile, the new lower quartile will be lower, therefore increasing the IQR.
Marks = 2