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Grade 12 Statistics Quiz

Dispersion, Ogives, Correlation and Regression

What this quiz covers

grade12_statistics_quiz1 draws its questions at random from a bank of 25 questions, with full worked solutions for every one.

Worked examples

A few of the question types, with full solutions, so you know what to expect.

Which measure of central tendency is most affected by an outlier?

  1. The mean
  2. The median
  3. The mode
  4. The interquartile range

Answer: The mean

\(\text{The mean uses EVERY value, so one extreme value drags it.}\)

\(\text{The median only depends on the middle position.}\)

Five salaries are R8 000; R9 000; R9 500; R10 000; R60 000. Which measure best describes the typical salary?

  1. The median, R9 500
  2. The mean, R19 300
  3. The mode
  4. The range, R52 000

Answer: The median, R9 500

\(\text{Mean}=\dfrac{96\,500}{5}=\text{R}19\,300\text{ — higher than four of the five salaries.}\)

\(\text{The R}60\,000 \text{ outlier has pulled the mean up.}\)

For the data \(12;\ 15;\ 17;\ 20;\ 22;\ 25;\ 30\), find \(Q_1\).

  1. 15
  2. 17
  3. 12
  4. 20

Answer: 15

\(\text{The median is }20\text{, so the lower half is } \{12;\ 15;\ 17\}.\)

\(Q_1 \text{ is the median of that half.}\)

For the same data, calculate the interquartile range.

  1. 10
  2. 18
  3. 5
  4. 20

Answer: 10

\(Q_1=15 \text{ and } Q_3=25\)

\(\text{IQR}=Q_3-Q_1=25-15\)

For the same data, calculate the range.

  1. 18
  2. 10
  3. 30
  4. 20

Answer: 18

\(\text{range}=\text{max}-\text{min}=30-12\)