دوره GRE Test- Practice & Study Guide ، فصل 25 : GRE Quantitative Reasoning- Probability and Statistics
دربارهی این فصل:
Looking for practice in probability and statistics for the GRE? This chapter offers engaging and fun video lessons to help prepare you for these questions on the GRE test. Test your knowledge with lesson quizzes and a chapter exam to help gauge your understanding of probability and statistics concepts.
Statistics Are on the Rise
When you decide to move to a new home, whether it is in the same city or across the country, one of the first things that you might do is look at the crime statistics for that area. Are they on the rise, or are they declining? You might also look at the schools. How do they stack up against other schools? Are their scores on the way down, or are they rising year after year?
All of this information, and information on almost any topic you can think of, can be found using statistics. Statistics is the study of the collection and analysis of data.
Relative and Cumulative Frequency
In mathematics, frequency refers to the number of times a particular event occurs. There are two types of frequency: relative and cumulative. Cumulative frequency is the total number of times a specific event occurs within the time frame given. Relative frequency is the number of times a specific event occurs divided by the total number of events that occur. Let’s use an example:
Your soccer team ended the season with a record of 15 wins and 3 losses. The cumulative frequency of your wins is 15 because that event occurred 15 times. The relative frequency of wins is 15 divided by 18, or 83%, because, out of the 18 total games (or events), your team won 15.
Relative frequency is a good way to predict how often an event might occur in the future. If you know that your soccer team has won 83% of the time in the past, you can reasonably assume that you will win 83% of the time in the future.
One of the best ways to tally and organize frequency data is to use a frequency table. A frequency table is a table that lists items and shows the number of times they occur. Below you see an example of a frequency table that describes the different ways students travel to get to school. You can also include a column that gives the relative frequency of each event.
Example of a frequency table
Let’s go back to our example of moving to a new town for a minute. If you were to read that the area you wanted to move to had a 2% increase in crime in the last year, you might think twice about moving there. At the very least, you would do some extra research.
What if you discovered in your additional research that the test scores at the local elementary school increased by 23% in the last year? That statistic might be more important to you than the small increase in crime in the same area. The percent increase represents the relative change between the old value and the new value. In order to calculate percent increase, you must have collected data about the same event, just at a different time.
Calculating Percent Increase
To determine the percent increase between two sets of data, you can use a frequency table and the following formula:
Percent Increase = Frequency 2 - Frequency 1 / Frequency 1 100.
Let’s try an example: Data for crime in a certain area was recorded over two years. The following table shows the occurrences of three different types of crime over a two-year period.
To calculate the percent increase, take each row individually and plug the numbers into the equation.
Percent increase of robbery = ((37 - 33) / 33) 100 = (4 / 33) 100 = 0.12 100 = 12%
Percent increase of murder = ((8 - 2) / 2) 100 = (6 / 2) 100 = 3 100 = 300%
Percent increase of assault = ((16 - 15) / 15) 100 = (1 / 15) 100 = 0.07 100 = 7%
Then, you can complete the table.
Here we have another example: 100 people were asked how often they ate dinner at home in a typical week. Then, they all took a class on how to cook healthy meals at home and after six months were asked again how often they ate at home. What was the percent increase for eating at home 5, 6 and 7 nights a week? Take a minute to try this one on your own.
Table corresponding to example problem above
And here you see the answers:
The percent increase for eating at home 5 nights a week was 347%, 6 nights a week - 350%, and 7 nights a week - 125%.
Determining the frequency and percent increase of events can be very helpful when trying to interpret certain sets of data. The cumulative frequency of a certain event is the number of times that event occurs in a certain time frame. Relative frequency refers to the percentage a certain event is of the total amount of events that occur. You can determine the percent increase of an event from time to time by using the formula:
Percent Increase = Frequency 2 - Frequency 1 / Frequency 1 100
این مجموعه تلوزیونی شامل 15 فصل زیر است:
In this lesson, we will examine two of the most widely used types of graphs- bar graphs and pie charts. These two graphs can provide the reader with a comparison of the different data that is displayed.
Measures of central tendency can provide valuable information about a set of data. In this lesson, explore how to calculate the mean, median, mode and range of any given data set.
Simple, compound, and complementary events are different types of probabilities. Each of these probabilities are calculated in a slightly different fashion. In this lesson, we will look at some real world examples of these different forms of probability.
To calculate the probability of a combination, you will need to consider the number of favorable outcomes over the number of total outcomes. Combinations are used to calculate events where order does not matter. In this lesson, we will explore the connection between these two essential topics.
In this lesson, you will learn how to calculate the probability of a permutation by analyzing a real-world example in which the order of the events does matter. We'll also review what a factorial is. We will then go over some examples for practice.
Sometimes probabilities need to be calculated when more than one event occurs. These types of compound events are called independent and dependent events. Through this lesson, we will look at some real-world examples of how to calculate these probabilities.
While the definition of factorial isn't complicated, it's easy to make them trickier by throwing a lot of them together and adding in some fractions. Test your skills here with some algebraic examples that make you use factorials without many numbers.
Maybe it's because I'm a math teacher, but when I watched the Olympics I found myself thinking about how many different ways the swimmers could have finished the race. In this video, you'll learn the answer to this question, why it's important and how it lead to the invention of the mathematical operation called the factorial.
Combinations are an arrangement of objects where order does not matter. In this lesson, the coach of the Wildcats basketball team uses combinations to help his team prepare for the upcoming season.
A permutation is a method used to calculate the total outcomes of a situation where order is important. In this lesson, John will use permutations to help him organize the cards in his poker hand and order a pizza.
Occasionally when calculating independent events, it is only important that the event happens once. This is referred to as the 'At Least One' Rule. To calculate this type of problem, we will use the process of complementary events to find the probability of our event occurring at least once.
Statistics is the study and interpretation of a set of data. One area of statistics is the study of probability. This lesson will describe how to determine the either/or probability of overlapping and non-overlapping events.
In this lesson, we will examine the meaning and process of calculating the standard deviation of a data set. Standard deviation can help to determine if the data set is a normal distribution.
In statistics, one way to describe and analyze data is by using frequency tables. This lesson will discuss relative and cumulative frequencies and how to calculate percent increase using these two methods.
Conditional probability, just like it sounds, is a probability that happens on the condition of a previous event occurring. To calculate conditional probabilities, we must first consider the effects of the previous event on the current event.
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