TMUA Data Analysis & Statistical Interpretation 4

Question 1

A linear regression line is given by ŷ = 3x + 7. A data point has x = 5, y = 28. What is the residual?

Accepted Answer

6

Answer

Predicted ŷ = 3(5)+7 = 22; residual = observed − predicted = 28−22 = 6.

Question 2

A pie chart shows 4 sectors. Three sectors have angles 90°, 120°, and 80°. What percentage of the data does the fourth sector represent?

Accepted Answer

25%

Answer

Fourth angle = 360−90−120−80 = 70°; percentage = 70/360×100 ≈ 19.4%.

Question 3

A dataset contains the values 3, 7, 7, 9, 12, 15. Which statement about the mode and median is correct?

Accepted Answer

Mode = 7, Median = 8

Answer

The mode is 7 (appears twice); median = average of 3rd and 4th values = (7+9)/2 = 8.

Question 4

The correlation coefficient between two variables is r = 0. What does this indicate?

Accepted Answer

There is no linear relationship between the variables

Answer

r = 0 indicates no linear correlation; a non-linear relationship may still exist.

Question 5

A survey finds that the mean weight of 40 students is 65 kg. Another group of 60 students has a mean weight of 70 kg. What is the combined mean weight?

Accepted Answer

68 kg

Answer

Combined mean = (40×65 + 60×70)/(100) = (2600+4200)/100 = 6800/100 = 68 kg.

(TMUA) Test of Mathematics for University Admission Practice Test

(TMUA) Test of Mathematics for University Admission Practice Test

TMUA Data Analysis & Statistical Interpretation 4