TMUA Data Analysis & Statistical Interpretation 2

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?

Accepted Answer

The change depends on the current sample size

Answer

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?

Accepted Answer

Students with lower scores watch more TV on average

Answer

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?

Accepted Answer

78

Answer

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?

Accepted Answer

22

Answer

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)?

Accepted Answer

0.70

Answer

P(A ∪ B) = P(A) + P(B) − P(A)P(B) = 0.4 + 0.5 − 0.2 = 0.7.

(TMUA) Test of Mathematics for University Admission Practice Test

(TMUA) Test of Mathematics for University Admission Practice Test

TMUA Data Analysis & Statistical Interpretation 2