MATH 110 Pre Exam Answer key, MATH 110: Introduction to Statistics, Portage Learning Statistics

MATH 110 Pre Exam Answer Key

, 1. Look at the following data and see if you can identify any outliers:
53 786 789 821 794 805 63 777 814 2333 783 811 795 788 780

The outliers are:
53 63 2333

2. Consider the following set of data:
{22, 14, 35, 49, 8, 18, 30, 44}
a) Find the median.

a) In order to find the median, we must first put the numbers in ascending

order: 8, 14, 18, 22, 30, 35, 44, 49.

Notice that there are two “middle” numbers, 22 and 30. The median is the average of these two
numbers. Median = (22+30)/2 = 26.

b) Find the mode of this set.

b) No number occurs more than once, so there is “no mode”.

3. Suppose A and B are two events with probabilities:

P(Ac )=.70,P(B)=.65,P(A∪B)=.80.


Find the following:
a) P(A∩B).

For P(A∩B). Use P(A∪B)=P(A)+P(B)-P(A∩B) and rearrange to
P(A∩B)=P(A)+P(B)-P(A∪B). But for this equation, we need P(A) which we can find by
using P(A)=1-P(Ac ). So, P(A)=1-.70= .30.


P(A∩B)=.30+.65-.80=.15.

b) P(A).

P(A) was found above as .30.

c) P(Bc).

For P(Bc ). Use P(B)=1-P(Bc ) which may be rearranged to (Bc )=1-P(B) .