TMUA Data Analysis & Statistical Interpretation 3 — Questions and Answers
Question 1: A box plot shows: minimum = 5, Q1 = 15, median = 25, Q3 = 40, maximum = 60. What is the range of the middle 50% of the data?
- 55
- 35
- 25 (Correct answer)
- 20
Correct answer: 25
The middle 50% spans from Q1 to Q3, giving IQR = 40 − 15 = 25.
Question 2: A histogram is positively skewed. Which ordering of the measures of centre is most likely correct?
- Mean < Median < Mode
- Mode < Median < Mean (Correct answer)
- Median < Mode < Mean
- Mean = Median = Mode
Correct answer: Mode < Median < Mean
In a positively (right) skewed distribution, the tail pulls the mean rightmost, so Mode < Median < Mean.
Question 3: A probability distribution table shows X taking values 1, 2, 3, 4 with probabilities 0.1, 0.3, 0.4, 0.2. What is E(X)?
- 2.5
- 2.7 (Correct answer)
- 2.9
- 3.0
Correct answer: 2.7
E(X) = 1(0.1)+2(0.3)+3(0.4)+4(0.2) = 0.1+0.6+1.2+0.8 = 2.7.
Question 4: In a sample of 200 students, 80 play sport and 60 play an instrument. If 30 do both, how many do neither?
- 60
- 90 (Correct answer)
- 70
- 50
Correct answer: 90
Students doing at least one activity = 80+60−30 = 110; neither = 200−110 = 90.
Question 5: Which measure of spread is most resistant to extreme outliers?
- Range
- Variance
- Standard deviation
- Interquartile range (Correct answer)
Correct answer: Interquartile range
The IQR uses only the middle 50% of data and is unaffected by extreme outliers.
Question 6: A stem-and-leaf diagram has stems 1, 2, 3 with leaves: 1|2 5 8, 2|0 3 3 7, 3|1 4. What is the median?
- 23 (Correct answer)
- 25
- 27
- 20
Correct answer: 23
The 9 values in order are 12,15,18,20,23,23,27,31,34; the median (5th value) is 23.
Question 7: Two datasets each have 10 values. Dataset A has variance 4; Dataset B has variance 9. A new dataset is formed by multiplying every value in A by 3. What is the new variance of A?
- 12
- 36 (Correct answer)
- 6
- 9
Correct answer: 36
Multiplying all values by k multiplies the variance by k², so new variance = 4×9 = 36.
TMUA Data Analysis & Statistical Interpretation 3
A box plot shows: minimum = 5, Q1 = 15, median = 25, Q3 = 40, maximum = 60.
What is the range of the middle 50% of the data?