TMUA Data Analysis & Statistical Interpretation 3

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?

Accepted Answer

25

Answer

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?

Accepted Answer

Mode < Median < Mean

Answer

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)?

Accepted Answer

2.7

Answer

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?

Accepted Answer

90

Answer

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?

Accepted Answer

Interquartile range

Answer

The IQR uses only the middle 50% of data and is unaffected by extreme outliers.

(TMUA) Test of Mathematics for University Admission Practice Test