Big Idea The distribution of the relative frequencies

of the outcomes from a situation can be displayed in tables and graphs.

GoalsCompare relative frequency, a ratio that

is calculated from actual data, with probability, and discuss the idea

of percentiles.

1. The dot plot shows the weights of 400,000 newborns in a given country over a six-year period. Every 10,000 births in a weight category are represented as a dot. The information, to the nearest 0.5 kg, is summarized in the table.

Birth Weight Number of What is the relative frequency of a newborn’s (kg) Births weight 2.5 20,000 a. being less than 3 kg? 3.0 80,000 b. being at least 3 kg? 3.5 150,000 c. being at most 3.5 kg? 4.0 90,000 d. having a weight w given 4.5 50,000 by 2.5 ≤ w ≤ 4.5? 5.0 10,000

2.5 3.0 3.5 4.0 4.5 5.0

2. Find the meaning of the 50th percentile in the newborn data and explain its meaning.

The 50th percentile is the least number thatis greater than or equal to 50% of the datavalues. There are 40 values, and 50% of

40 = 20, so look at the 20th weight from thebottom of the list. This weight is 3.5 kg.

So 3.5 kg is the 50th percentile of newbornweights. Thus, 50 % of the newborn babies

weighed less than 3.5 kg.

Percentile: The pth percentile of a a data setis the smallest data value that is greaterthan or equal to p percent of the data values.

Relative Frequency1. Calculated from data

2. The ratio of the number of timesan event has occurred to the # oftimes it could occur

3. 0 means that an event did notoccur. 1 means that the event occurred every time it could.4. The more often an event occursrelative to the number of times it could occur, the closer its relative frequency is to 1.5. The sum of the relative frequencies of alloutcomes in an experiment is 1.

6. If the relative frequency of an event is r, then the relative frequency of its complement is 1 - r .

Probability1. Deduced from assumptions (likerandomness) or assumed to be close to some relative frequency2. If outcomes are equally likely, the ratio of the number of outcomes in an event to the total number of possible outcomes3. 0 means that an event is impossible.1 means that an event is sure to happen.4. The more likely an event is, the closer its probability is to 1.

5. The sum of the probabilities of alloutcomes in an experiment is 1.

6. If the probability of an event is p,then the probability of its complement is 1 - p.