HAPPY FRIDAY THE 13th!!!!!
February 13, 2009
Conditional Probability/Analyzing Data
REMINDER:

If A and B are mutually exclusive events:

If A and B are not mutually exclusive events
REMEMBER:

Example 1: About 53% of U.S. college students
are under 25 years old. About 21% of U.S. college
students are over 34 years old. What is the
probability that a college student chosen at
random is under 25 or over 34?

Example 2: Suppose you reach into a bowl of 3
red apples, 3 green apples, 1 lime, 1 lemon, and 2
oranges. What is the probability that the fruit is
an apple or green?
REMEMBER:

: “the probability of the event B, given
the event A”

Formula:

Researchers asked people who exercise
regularly whether they jog or walk. Fiftyeight percent of the respondents were male.
Twenty percent of all respondents were
males who said that they jog. Find the
probability that a male respondent jogs.

A student in Buffalo, New York, made the
observations below:
◦ Of all snowfalls, 5% are heavy (at least 6 in.)
◦ After a heavy snowfall, schools are closed 67% of the time
◦ After a light snowfall (less than 6 in.) schools are closed 3%
of the time.
Find the probability that the snowfall is light and
the schools are open.

Look over last night’s homework with the
people next to you.

Ask questions and help each other with the
problems you struggled with last night.
Analyzing Data
Measures of central tendency help describe a
data set
 Mean: the average of all the data values

Median: middle value or mean of the two
middle values

Mode: the most frequently occurring value

Find the mean, median, and mode for the
following values:
1.
98, 95, 99, 97, 89, 92, 97, 62, 90
2.
2.4, 4.3, 3.7, 3.9, 2.8, 5.4, 2.8

There are 5 parts to a box and whisker plot:
1.
Minimum Value
Quartile 1 (Q1): The median of the lower half
Quartile 2 (Q2): The median of the entire
data set
Quartile 3 (Q3): The median of the upper half
Maximum Value
2.
3.
4.
5.
Median of the lower part
(Q1) = 83
Median of the upper part
(Q3) = 83
56 58 58 63 65 71 74 78 82 84 85 86
Median of the set of
data (Q2) = 72.5

Make a box-and-whisker plot for the
following values:
84, 79, 90, 73, 95, 88, 92, 81, 67

Percentile: a number that indicates the
percent of data that is less than or equal to a
particular number in the data set.

Find the values at the 20th and 65th
percentiles for the following values:
54, 98, 45, 87, 98, 64, 21, 61, 71, 82, 93, 65, 98, 87,
24, 65, 97, 31, 47

Step 1: Put the values in numerical order:
21, 24, 31, 45, 47, 54, 61, 62, 64, 65, 65, 71, 82, 87, 87, 93, 97, 98, 98, 98

Step 2: Find the number of values that fall below
the 20th percentile and the number of values that
fall below the 65th percentile

Find the value at the 0th percentile of the last
data set.

Find the value at the 45th percentile of the last
data set.

Outlier: An item of a data set with a value
substantially different from the rest of the
items in the data set.

Find the outlier for this set of values. Describe
how it would affect the mean of the data:
56, 65, 73, 59, 98, 65, 59

Suppose the values in Example 6 are
measurements of the water temperature of a
lake. Would you discard the outlier? Why?

Suppose the data represent the number of
customers in a small restaurant each night
during one week. Would you discard the
outlier? Why?
Pg 664 #1, 2, 4, 5, 8-10,
12, 14-17, 19