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Date	May 2021	Marks available	3	Reference code	21M.1.SL.TZ1.4
Level	Standard Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 1
Command term	Find	Question number	4	Adapted from	N/A

Question

A research student weighed lizard eggs in grams and recorded the results. The following box and whisker diagram shows a summary of the results where $L$ and $U$ are the lower and upper quartiles respectively.

The interquartile range is $20$ grams and there are no outliers in the results.

Find the minimum possible value of $U$ .

[3]

a.

Hence, find the minimum possible value of $L$ .

[2]

b.

Markscheme

attempt to use definition of outlier

$1.5 \times 20 + Q_{3}$ (M1)

$1.5 \times 20 + U \geq 75$ ( $\Rightarrow U \geq 45$ , accept $U > 45$ ) OR $1.5 \times 20 + Q_{3} = 75$ A1

minimum value of $U = 45$ A1

[3 marks]

a.

attempt to use interquartile range (M1)

$U - L = 20$ (may be seen in part (a)) OR $L \geq 25$ (accept $L > 25$ )

minimum value of $L = 25$ A1

[2 marks]

b.

Examiners report

[N/A]

a.

[N/A]

b.

Syllabus sections

Topic 4—Statistics and probability » SL 4.1—Concepts, reliability and sampling techniques

Show 29 related questions

EXM.1.SL.TZ0.2c:
Give an example of a set of data with 7 numbers in it that does have an outlier, justify this fact by stating the Interquartile Range.
EXM.2.SL.TZ0.1c:
State the name for this type of sampling technique.
EXM.2.SL.TZ0.1a:
State the name for this type of sampling technique.
EXM.2.SL.TZ0.1d.i:
Calculate Pearson’s product moment correlation coefficient, $r$ .
18M.1.SL.TZ1.S_2a:
Find the value of the interquartile range.
19M.2.SL.TZ1.S_3b:
The graph of $f$ has a horizontal tangent line at $x = 0$ and at $x = a$ . Find $a$ .
17M.2.SL.TZ1.S_1b.i:
Find the mean.
17M.2.SL.TZ2.S_8b.i:
Write down the coordinates of A.
17M.2.SL.TZ2.S_8c.i:
Find the coordinates of B.
EXM.2.SL.TZ0.1b.i:
Show that 3 students will be selected from grade 12.
EXM.2.SL.TZ0.1d.iii:
Explain why the value of $r$ makes it appropriate to find the equation of a regression line.
EXM.2.SL.TZ0.1b.ii:
Calculate the number of students in each grade in the sample.
EXM.1.SL.TZ0.2b:
Hence, show that a data set with only 5 numbers in it cannot have any outliers.
17M.2.SL.TZ2.S_8b.ii:
Write down the rate of change of $f$ at A.
EXM.2.SL.TZ0.1d.ii:
Interpret the meaning of the value of $r$ in the context of the principal’s concerns.
EXM.1.SL.TZ0.2a:
Recalling definitions, such as the Lower Quartile is the $\frac{{n + 1}}{4}th$ piece of data with the data placed in order, find an expression for the Interquartile Range.
17M.2.SL.TZ2.S_8a:
Find the value of $p$ .
17M.2.SL.TZ2.S_8d:
Let $R$ be the region enclosed by the graph of $f$ , the $x$ -axis, the line $x = b$ and the line $x = a$ . The region $R$ is rotated 360° about the $x$ -axis. Find the volume of the solid formed.
17M.2.SL.TZ1.S_1a.ii:
Find the value of the range.
22M.2.SL.TZ2.5b:
Verify that the measurement of $0.46$ seconds is not an outlier.
17M.2.SL.TZ1.S_1a.i:
Write down the mode.
21M.1.SL.TZ1.4b:
Hence, find the minimum possible value of $L$ .
18M.1.SL.TZ1.S_2b:
One student sent k text messages, where k > 11 . Given that k is an outlier, find the least value of k.
17M.2.SL.TZ2.S_8c.ii:
Find the the rate of change of $f$ at B.
21M.1.SL.TZ2.7e.i:
Explain why this sampling method might not provide an accurate representation of the amount of time all of the students in the school spend doing homework.
21M.1.SL.TZ2.7e.ii:
Suggest a more appropriate sampling method.
EXM.2.SL.TZ0.1e:
Another student at the school, Jasmine, has a self-esteem value of 29.

By finding the equation of an appropriate regression line, estimate the time Jasmine spent on social media the previous day.
22M.1.SL.TZ1.3a:
Find the largest value of $c$ that would not be considered an outlier.
17M.2.SL.TZ1.S_1b.ii:
Find the variance.

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