Question 1
The box plot below was created based on the scores achieve by a class of Year 8s in their maths test.
What is the range of their test results?
Select the correct answer from the list below:
A: 14
B: 19
C: 21
D: 18
CORRECT ANSWER: C: 21
WORKED SOLUTION:
We find the range by subtracting the smallest value from the largest. Our largest value is 74 and our smallest value is 53.
74-53=21
Level 6
Question 2
The box plot below was created based on the scores achieve by a class of Year 8s in their maths test.
Find the inter-quarterfinal range.
Select the correct answer from the list below:
A: 14
B: 19
C: 21
D: 18
CORRECT ANSWER: A: 14
WORKED SOLUTION:
We find the IQR (inter-quarterfinal range) by subtracting the lower quartile from the upper quartile.
Q1=56 is the lower quartile.
Q3=70 is the upper quartile.
Q3-Q1 = 70 -56 = 14
Level 6
Question 3
200 participants take part in a 10km race.
Their times were collected, and the following information was found to the nearest minute:
Slowest runner: 85 minutes.
Upper quartile: 76 minutes.
Median: 68 minutes.
Range: 33 minutes.
IQR: 17 minutes.
Use this information to construct a box plot.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: D
WORKED SOLUTION:
We are told that the slowest runner (which will be the highest value) took 85 minutes, so we know that the end of our box plot will be at 85.
Next, we are told that the upper quartile is 76, so we can put that in.
And we’re also told the median, so we can put that in.
But now, we’re missing two things, the lower quartile and the smallest value. Luckily, we can find these using the rest of the information we’re given.
Lower Quartile
Q_3-Q_1=IQR
76-Q_1=17
76 =17+ Q_1
76 -17=Q_1
59=Q_1
Now that we have our lower quartile, we can put this in.
Smallest value
Largest-Smallest=Range
85-Smallest=33
85 =33+Smallest
85 -33=Smallest
52=Smallest
Now that we have the smallest value, we can put this in.
And finally, we just need to connect everything accordingly.
Level 6
Question 4
A car company releases a new model of car, the following information is provided about the cost of these cars in £1000s:
Cheapest model: 25
Lower quartile: 31
Median: 45
Range: 29 minutes.
IQR: 19 minutes.
Construct a box plot using this information.
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: A
WORKED SOLUTION:
We are told that the cheapest model (which will be the lowest value) us 25 (£1000), so we know that the start of the box plot must be at 25.
Next, we are told that the lower quartile is 31, so we can put that in.
And we’re also told the median, so we can put that in.
But now, we’re missing two things, the upper quartile and the largest value. Luckily, we can find these using the rest of the information we’re given.
Lower Quartile
Q_3-Q_1=IQR
Q_3-31=19
Q_3=19+31
Q_3=50
Now that we have our upper quartile, we can put this in.
Largest value
Largest-Smallest=Range
Largest-25 =29
Largest =29+25
Largest =54
Now that we have the largest value, we can put this in.
And finally, we just need to connect everything accordingly.
Level 6
Question 5
A group of students are guessing the age of their supply teacher. Use their guesses to construct a box plot.
21, 25, 27, 28, 28, 28, 28, 30, 31, 33, 45Select the correct answer from the list below:
A:
B:
C:
D: None of the above
CORRECT ANSWER: C
WORKED SOLUTION:
The five things we need to know to construct a box plot are: Smallest value, lower quartile, median, upper quartile, and largest value.
We can read of the smallest and largest values quite easily: 21 and 45, so we can put those straight on.
Now we need to find the lower quartile, median, and upper quartile.
Median
We can find the median in two ways: either strike off until we get to the middle, or use our n+1 method where we divide by 2. Here, n=11 because we have 11 pieces of data.
n+1=11+1
11+1=12
And now we divide by 2.
So, we want our 6th piece of data:
21, 25, 27, 28, 28, 28, 28, 30, 31, 33, 45Which is 28.
Now, we can use a similar method to find the lower and upper quartiles.
Lower Quartile
12\div4=3 21, 25, 27, 28, 28, 28, 28, 30, 31, 33, 45
The lower quartile is 27.
Upper Quartile
12\div4=3
3\times3=9
The upper quartile is 31.
And now, we just need to connect the pieces.
Level 6
Question 6
The following scores on an English test were achieved by 7 boys on a test with 100 marks.
51, 59, 63, 75, 77, 78, 80Construct a box plot using this information to compare the boys with the girls, whose score gave the following box plot:
Select the correct answer from the list below:
A:
B:
C:
D:
CORRECT ANSWER: A
WORKED SOLUTION:
The five things we need to know to construct a box plot are: Smallest value, lower quartile, median, upper quartile, and largest value.
We can read of the smallest and largest values quite easily: 51 and 80, so we can put those straight on.
Now we need to find the lower quartile, median, and upper quartile.
Median
We can find the median in two ways: either strike off until we get to the middle or use our n+1 method where we divide by 2. Here, n=7 because we have 7 pieces of data.
n+1=7+1
7+1=8
And now we divide by 2.
So, we want our 4th piece of data:
51, 59, 63, 75, 77, 78, 80
Which is 75.
Now, we can use a similar method to find the lower and upper quartiles.
Lower Quartile
8\div4=251, 59, 63, 75, 77, 78, 80
The lower quartile is 59.
Upper Quartile
8\div4=2
2\times3=6
51, 59, 63, 75, 77, 78, 80
The upper quartile is 78.
And now, we just need to connect the pieces.
And now we can compare the boys and girls.
We can see that the highest score for the boys was higher than for the girls, but the boys also scored the lowest score.
We can also see that the spread of scores is much higher for the boys than for the girls.
Level 6