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Data Handling, Statistics and Mathematical Skills

Mathematical requirements (Appendix A): Calculations for statistical tests

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Recall questions on Mathematical requirements: Calculations for statistical tests.

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Numbers

Condition A totals 90 and condition B totals 60, each across the same 6 participants. Calculate both means and the difference between them.

Numbers

Using df = (R − 1)(C − 1), a contingency table with 3 rows gives 6 degrees of freedom. How many columns did it have?

Numbers

A category accounts for 35% of the data. Calculate the angle of its sector in a pie chart.

Questions from this subtopic

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  1. 1

    Condition A totals 90 and condition B totals 60, each across the same 6 participants. Calculate both means and the difference between them.

    Model answer

    The mean of condition A is 15, the mean of condition B is 10, and the difference between them is 5.

  2. 2

    In a contingency table the row total is 40, the column total is 30 and the grand total is 100. Calculate the expected frequency for that cell.

    Model answer

    The expected frequency is 40 × 30 ÷ 100 = 12.

  3. 3

    For one cell of a Chi Square table the observed frequency is 18 and the expected frequency is 12. Calculate (O − E)² ÷ E for that cell.

    Model answer

    The difference is 6, so 6² ÷ 12 = 36 ÷ 12 = 3.

  4. 4

    Using df = (R − 1)(C − 1), a contingency table with 3 rows gives 6 degrees of freedom. How many columns did it have?

    Model answer

    Since (3 − 1) × (C − 1) = 6, then C − 1 = 3 and the table had 4 columns.

  5. 5

    A category accounts for 35% of the data. Calculate the angle of its sector in a pie chart.

    Model answer

    The sector angle is 0.35 × 360° = 126°.

  6. 6

    Of 60 respondents, 15 chose one option. Calculate the angle of that sector in a pie chart.

    Model answer

    15 out of 60 is 25%, so the sector angle is 90°.

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AThe mean of condition A is 15.
BThe mean of condition B is 10.
CThe difference between them is 5.

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