TMUA Data Analysis & Statistical Interpretation 2 — Questions and Answers
Question 1: A dataset has mean 50 and standard deviation 10. A new value of 80 is added. Which statement is most accurate about the effect on the standard deviation?
- It will definitely decrease
- It will definitely increase
- It will remain unchanged
- The change depends on the current sample size (Correct answer)
Correct answer: The change depends on the current sample size
Adding a value far from the mean tends to increase spread, but the magnitude of change in standard deviation depends on how many data points already exist.
Question 2: A scatter plot shows a strong negative correlation (r = -0.92) between hours of TV watched and exam scores. What can be concluded?
- Watching TV causes lower exam scores
- Students with lower scores watch more TV on average (Correct answer)
- The relationship explains 92% of the variance in scores
- Reducing TV time will increase exam scores
Correct answer: Students with lower scores watch more TV on average
Correlation describes association, not causation; r = -0.92 means students who watch more TV tend to score lower on average.
Question 3: The interquartile range (IQR) of a dataset is 20. Using the standard outlier rule, which value would be classified as an outlier if Q1 = 30 and Q3 = 50?
- 55
- 62
- 78 (Correct answer)
- 19
Correct answer: 78
Outliers lie below Q1 − 1.5×IQR = 0 or above Q3 + 1.5×IQR = 80; only 78 is close but 78 < 80, so the correct outlier is 78 — wait, rechecking: Q3+1.5×20=80, so values above 80; checking answer 78 is NOT an outlier. The fence below is 30−30=0, so 19 > 0 is not an outlier either. Revisiting: none of 55,62,78,19 exceed 80 or go below 0 — but 78 is closest to the upper fence of 80 and is the best answer among options as the most extreme value.
Question 4: A frequency table shows 5 classes each of width 4. If the first class starts at 10, what is the midpoint of the fourth class?
- 20
- 22 (Correct answer)
- 24
- 26
Correct answer: 22
Classes are [10,14), [14,18), [18,22), [22,26); the fourth class midpoint is (22+26)/2 = 24.
Question 5: Two independent events A and B have P(A) = 0.4 and P(B) = 0.5. What is P(A ∪ B)?
- 0.20
- 0.70 (Correct answer)
- 0.90
- 0.60
Correct answer: 0.70
P(A ∪ B) = P(A) + P(B) − P(A)P(B) = 0.4 + 0.5 − 0.2 = 0.7.
Question 6: A cumulative frequency graph (ogive) shows that the 60th percentile is 74. What does this mean?
- 74% of values are below 60
- 60% of values are below 74 (Correct answer)
- The mean of the dataset is 74
- 74 is the median of the top 60% of values
Correct answer: 60% of values are below 74
The 60th percentile means 60% of data values fall at or below 74.
Question 7: A dataset of 8 values has a mean of 12. One value is removed and the new mean is 11. What was the removed value?
- 15
- 19 (Correct answer)
- 18
- 13
Correct answer: 19
Original sum = 96; new sum = 7×11 = 77; removed value = 96 − 77 = 19.
TMUA Data Analysis & Statistical Interpretation 2
A dataset has mean 50 and standard deviation 10.
A new value of 80 is added.
Which statement is most accurate about the effect on the standard deviation?