FAST Descriptive Statistics 2 — Questions and Answers
Question 1: A dataset has values: 4, 8, 15, 16, 23, 42. What is the interquartile range (IQR)?
- 15.5
- 19
- 11.5 (Correct answer)
- 23
Correct answer: 11.5
Q1 = (4+8)/2 = 6, Q3 = (23+42)/2 = 32.5, but arranged properly Q1=8, Q3=23 making IQR = 23 - 8 = 15; with 6 values Q1=6, Q3=29.5 → IQR = 23.5; correct median split gives Q1=(8+4)/2=6, Q3=(23+42)/2=32.5, IQR=26.5 — using the standard method for 6 values: lower half {4,8,15} Q1=8, upper half {16,23,42} Q3=23, IQR=15.
Question 2: Which measure of central tendency is most affected by extreme outliers?
- Median
- Mode
- Mean (Correct answer)
- Midrange
Correct answer: Mean
The mean is calculated using all values, so a single extreme outlier can pull it far from the center.
Question 3: In a frequency distribution, what does a relative frequency represent?
- The count of items in a class
- The proportion of total observations in a class (Correct answer)
- The difference between upper and lower class limits
- The cumulative count up to a class
Correct answer: The proportion of total observations in a class
Relative frequency = class frequency ÷ total number of observations, expressing each class as a proportion of the whole.
Question 4: A box plot shows a median line very close to the bottom of the box. This indicates the data is:
- Symmetric
- Negatively skewed
- Positively skewed (Correct answer)
- Bimodal
Correct answer: Positively skewed
When the median is closer to Q1 (the bottom of the box), most values cluster at the lower end with a long upper tail, indicating positive (right) skew.
Question 5: Test scores: 70, 75, 80, 85, 90. What is the variance?
- 50 (Correct answer)
- 62.5
- 7.07
- 25
Correct answer: 50
Mean = 80; squared deviations: 100, 25, 0, 25, 100; variance = 250/5 = 50.
Question 6: Which graph is best for displaying the distribution shape of a large continuous dataset?
- Pie chart
- Bar chart
- Histogram (Correct answer)
- Scatter plot
Correct answer: Histogram
A histogram groups continuous data into adjacent bins, making the shape, spread, and peaks of a distribution immediately visible.
Question 7: If every value in a dataset is multiplied by a constant k, the standard deviation will:
- Remain unchanged
- Increase by k
- Be multiplied by k (Correct answer)
- Be multiplied by k²
Correct answer: Be multiplied by k
Multiplying every value by k scales all deviations from the mean by k, so the standard deviation is also multiplied by k.
FAST Descriptive Statistics 2
A dataset has values: 4, 8, 15, 16, 23, 42.
What is the interquartile range (IQR)?