NSAA NSAA Mathematics - Statistics and Probability 3

Question 1

The mode of the data set {4, 7, 7, 3, 4, 7, 9} is:

Accepted Answer

7

Answer

7 appears three times, more than any other value, so the mode is 7.

Question 2

A box has 3 defective and 7 non-defective items. Two items are drawn without replacement. What is the probability both are defective?

Accepted Answer

1/15

Answer

P(both defective) = (3/10) × (2/9) = 6/90 = 1/15.

Question 3

Which of the following is the correct definition of standard deviation?

Accepted Answer

The square root of the variance

Answer

Standard deviation is the square root of the variance, measuring spread around the mean.

Question 4

If a data set has a positive skew, which relationship is typically true?

Accepted Answer

Mode < Median < Mean

Answer

In a positively skewed distribution, the tail extends to the right, pulling the mean above the median, which is above the mode.

Question 5

What is the expected value of a fair six-sided die roll?

Accepted Answer

3.5

Answer

E(X) = (1+2+3+4+5+6)/6 = 21/6 = 3.5.

NSAA - Natural Sciences Admissions Assessment Practice Test