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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) = \begin{cases} k \sin \left( \dfrac{\pi x}{6} \right), & 0 \leqslant x \leqslant 6 \\ 0, & \text{otherwise} \end{cases}

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 mode of $X$ .

[1]

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

[4]

Hence state the interquartile range of $X$ .

[3]

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

[2]

Question 2

SLPaper 1

Deb used a thermometer to record the maximum daily temperature over ten consecutive days. Her results, in degrees Celsius (${}^\circ\text{C}$), 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 consists of five numbers $x_1, x_2, x_3, x_4, x_5$ 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.

$$11 \quad 13 \quad 8 \quad 11 \quad 8 \quad 7 \quad 8 \quad 14 \quad x \quad 15$$

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

Find the value of $x$.

[2]

Find the standard deviation.

[2]

Find the interquartile range.

[2]

Paper

Level

Question 1

HLPaper 1

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

f(x) = \begin{cases} k \sin \left( \dfrac{\pi x}{6} \right), & 0 \leqslant x \leqslant 6 \\ 0, & \text{otherwise} \end{cases}

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 mode of $X$ .

[1]

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

[4]

Hence state the interquartile range of $X$ .

[3]

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

[2]

Question 2

SLPaper 1

Deb used a thermometer to record the maximum daily temperature over ten consecutive days. Her results, in degrees Celsius (${}^\circ\text{C}$), 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 consists of five numbers $x_1, x_2, x_3, x_4, x_5$ 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.

$$11 \quad 13 \quad 8 \quad 11 \quad 8 \quad 7 \quad 8 \quad 14 \quad x \quad 15$$

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

Find the value of $x$.

[2]

Find the standard deviation.

[2]

Find the interquartile range.

[2]

Paper

Level

Question 1

HLPaper 1

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

f(x) = \begin{cases} k \sin \left( \dfrac{\pi x}{6} \right), & 0 \leqslant x \leqslant 6 \\ 0, & \text{otherwise} \end{cases}

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 mode of $X$ .

[1]

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

[4]

Hence state the interquartile range of $X$ .

[3]

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

[2]

Question 2

SLPaper 1

Deb used a thermometer to record the maximum daily temperature over ten consecutive days. Her results, in degrees Celsius (${}^\circ\text{C}$), 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 consists of five numbers $x_1, x_2, x_3, x_4, x_5$ 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.

$$11 \quad 13 \quad 8 \quad 11 \quad 8 \quad 7 \quad 8 \quad 14 \quad x \quad 15$$

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

Find the value of $x$.

[2]

Find the standard deviation.

[2]

Find the interquartile range.

[2]

SL 4.3—Mean, median, and mode Questionbank