Averages of Statistical Data practice questions

Secondary 2 topics, working towards 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 averages of statistical data free

What this topic covers

Worked examples

Example 1

The table below shows the distribution of the correct answers out of six of a group of students. <table style="border-collapse: collapse; width: 100%; max-width: 500px; margin: 0.5rem 0;"><thead><tr style="background: rgba(59, 130, 246, 0.1);"><th style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">Correct answers</th><th style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">Frequency</th></tr></thead><tbody><tr><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">1</td><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">13</td></tr><tr><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">2</td><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">9</td></tr><tr><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">3</td><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;"><i>x</i></td></tr><tr><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">4</td><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">2</td></tr><tr><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">5</td><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">9</td></tr><tr><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">6</td><td style="border: 1px solid #e2e8f0; padding: 6px 12px; text-align: center;">7</td></tr></tbody></table> The mode of the distribution is 1. Find the greatest possible value of <i>x</i>.
Show the worked solution
  • Forthemodetoremain1,itsfrequency(13)mustbestrictlygreaterthanallotherfrequencies.For the mode to remain 1, its frequency (13) must be strictly greater than all other frequencies.
  • The frequency of value 3 is <i>x</i>, so we need $x < 13$.
  • Since <i>x</i> must be a whole number, the greatest possible value is $x = 12$.
  • $x = 12$

Answer: 1212

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

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.

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