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SL 4.3—Mean, median, and mode - IB Questionbank | RevisionDojo

Practice SL 4.3—Mean, median, and mode with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

HLPaper 1

The continuous random variable X has a probability density function given by

$f(x) = \left\{ {\begin{array}{*{20}{l}} {k\sin \left( {\frac{{\pi x}}{6}} \right),}&{0 \leqslant x \leqslant \,6} \\ {0,}&{{\text{otherwise}}} \end{array}} \right.$ .

Find the value of $k$ .

[4]

By considering the graph of f write down the mean of $X$ ;

[1]

By considering the graph of f write down the median of $X$ ;

[1]

By considering the graph of f write down the modeof $X$ .

[1]

Show that $P(0 \leqslant X \leqslant 2) = \frac{1}{4}$ .

[4]

Hence state the interquartile range of $X$ .

[2]

Calculate $P(X \leqslant 4|X \geqslant 3)$ .

[2]

Question 2

SLPaper 1

Deb used a thermometer to record the maximum daily temperature over ten consecutive days.Her results, in degrees Celsius ( $° C$ ), are shown below.

$14, 15, 14, 11, 10, 9, 14, 15, 16, 13$

For this data set, find the value of

the mode.

[1]

the mean.

[2]

the standard deviation.

[1]

Question 3

SLPaper 1

A set of data comprises of five numbers ${x_{1\,}}{\text{,}}\,\,{x_2}{\text{,}}\,\,{x_3}{\text{,}}\,\,{x_4}{\text{,}}\,\,{x_5}$ which have been placed in ascending order.

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.

[2]

Hence, show that a data set with only 5 numbers in it cannot have any outliers.

[5]

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.

[2]

Question 4

SLPaper 1

Each month the number of days of rain in Cardiff is recorded.
The following data was collected over a period of 10 months.

11 13 8 11 8 7 8 14 x 15

For these data the median number of days of rain per month is 10.

Find the value of x.

[2]

Findthe standard deviation

[2]

Findthe interquartile range.

[2]

SL 4.3—Mean, median, and mode Questionbank