1. Big Idea The distribution of the relative frequencies of the outcomes from a situation can be displayed in tables and graphs. Goals Compare relative frequency, a ratio that is calculated from actual data, with probability, and discuss the idea of percentiles.

2. 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      

3. 2. Find the meaning of the 50th percentile in the newborn data and explain its meaning. The 50 th percentile is the least number that is greater than or equal to 50% of the data values. There are 40 values, and 50% of 40 = 20, so look at the 20 th weight from the bottom of the list. This weight is 3.5 kg. So 3.5 kg is the 50 th percentile of newborn weights. Thus, 50 % of the newborn babies weighed less than 3.5 kg. Percentile: The pth percentile of a a data set is the smallest data value that is greater than or equal to p percent of the data values.

4. Relative Frequency 1. Calculated from data 2. The ratio of the number of times an event has occurred to the # of times it could occur 3. 0 means that an event did not occur. 1 means that the event occurred every time it could. 4. The more often an event occurs relative to the number of times it could occur, the closer its relative frequency is to 1. 5. The sum of the relative frequencies of all outcomes 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. Probability 1. Deduced from assumptions (like randomness) or assumed to be close to some relative frequency 2. If outcomes are equally likely, the ratio of the number of outcomes in an event to the total number of possible outcomes 3. 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 all outcomes in an experiment is 1. 6. If the probability of an event is p, then the probability of its complement is 1 - p.