Statistical Data Analysis practice questions

Secondary 4 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise statistical data analysis free

What this topic covers

Box-and-Whisker Plots
Cumulative Frequency Tables and Curves
Median, Quartiles, Percentiles, Range and IQR
Standard Deviation

Worked examples

Example 1

The following data shows the heights, in cm, of some seedlings.

8,\ 10,\ 17,\ 23,\ 24,\ 29,\ 31,\ 32,\ 36,\ 58,\ 59,\ 60

Find the range.

Show the worked solution

$Arrange the data in ascending order:$
$8,\ 10,\ 17,\ 23,\ 24,\ 29,\ 31,\ 32,\ 36,\ 58,\ 59,\ 60$
$Number of values: $n = 12$$
$Minimum value $= 8$$
$Maximum value $= 60$$
$\text{Range} = \text{Maximum} - \text{Minimum}$
$$= 60 - 8$$
$$= 52$$

Answer: $52$

Example 2

The data below shows the heights of seedlings (in cm) of a sample of 12 readings.

8,\ 16,\ 22,\ 26,\ 30,\ 33,\ 38,\ 40,\ 42,\ 44,\ 46,\ 48

Find the interquartile range (IQR).

Show the worked solution

$Arrange the data in ascending order ($n = 12$):$
$8,\ 16,\ 22,\ 26,\ 30,\ 33,\ 38,\ 40,\ 42,\ 44,\ 46,\ 48$
$For $n = 12$ values, split into two halves of $6$ values each. $Q_1$ is the median of the lower half and $Q_3$ is the median of the upper half.$
$Lower half: $8,\ 16,\ 22,\ 26,\ 30,\ 33$$
$Q_1$ is the mean of the 3rd and 4th values of the lower half: $Q_1 = \dfrac{22 + 26}{2} = 24$
$Upper half: $38,\ 40,\ 42,\ 44,\ 46,\ 48$$
$Q_3$ is the mean of the 3rd and 4th values of the upper half: $Q_3 = \dfrac{42 + 44}{2} = 43$
$\text{IQR} = Q_3 - Q_1$

Answer: $19$

Questions parents ask

Is it really free?

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.