Measures of central tendency and dispersion; outliers practice questions.

A data set has lower quartile Q1 = 7 and upper quartile Q3 = 10. Using the rule Q3 + 1.5 × IQR, determine the value above which a data point is classified as an outlier.

• 11.5
• 14.5
• 25
• 4.5

Answer: 14.5

IQR = Q3 - Q1 = 3, so the upper boundary is 10 + 1.5 × 3 = 14.5. Any value above 14.5 is an outlier.

A teacher rescales test marks using the rule: new mark = 2 × (old mark) - 4. The standard deviation of the old marks was 3. Determine the standard deviation of the new marks.

• 2
• 3
• 6
• 36

Answer: 6

Multiplying by 2 doubles the standard deviation to 6; subtracting 4 shifts all values equally and has no effect on spread.

The number of books read in a month by 20 students is summarised in a frequency table: 1 book (3 students), 2 books (5 students), 3 books (7 students), 4 books (5 students). Calculate the mean number of books read.

• 2.7
• 2.5
• 3
• 13.5

Answer: 2.7

Total books = 1×3 + 2×5 + 3×7 + 4×5 = 54, and 54 ÷ 20 = 2.7. Each value must be weighted by its frequency, not averaged directly.

Class A has 10 students with a mean score of 6. Class B has 15 students with a mean score of 8. Calculate the mean score of all 25 students combined.

• 7
• 7.5
• 14
• 7.2

Answer: 7.2

Total score = 10×6 + 15×8 = 180, so the combined mean is 180 ÷ 25 = 7.2. Averaging 6 and 8 directly ignores the different group sizes.

A single extreme value is added to a large data set. Which measure is most strongly affected by this new value?

• The mean
• The median
• The mode
• The interquartile range

Answer: The mean

The mean uses every value in its calculation, so one extreme value can pull it substantially. The median, mode and IQR are resistant to outliers.

The variance of a data set is 49. Determine the standard deviation.

• 24.5
• 7
• 98
• 2401

Answer: 7

Standard deviation is the square root of the variance: √49 = 7. Halving or squaring the variance are common errors.