Back To CourseContemporary Math: Help and Review
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Beverly has taught mathematics at the high school level and has a doctorate in teaching and learning.
Timmy is a pizza shop manager and he has two locations picked for a possible new location. He decides to conduct a mini-study to decide based on a variety of factors. Location A is smaller, and he notices that there is a high school two blocks away, some business offices close by, and a laundromat next door. Location B is larger and next to a supermarket with some business offices scattered around the area, amidst several vacant lots. If you were Timmy, which would you choose?
You are a statistician in many ways. Statistics is the method of conducting a study about a particular topic by collecting, organizing, interpreting, and finally presenting data. Being a statistician at an elementary level may simply mean noticing patterns in daily circumstances and drawing conclusions about those patterns. On a grander scale, statisticians may spend months or years conducting a study before they can produce meaningful analysis of information. Statistics is its own community, with rules, procedures, and policies all built on simple mathematical principles.
The statistical process guides genuine study, and statisticians are exacting in their methodologies. The major steps of statistics are explained in a simplistic form as follows:
Other than individuals and small businesses owners like Timmy who conducted their own studies, there are some entities who thrive on statistics. Here are a few major examples.
The government uses statistics to make decisions about populations, health, education, etc. It may conduct research on education to check the progress of high schools students using a specific curriculum or collect characteristic information about the population using a census.
The medical field would be far less effective without research to see which medicines or interventions work best and how the human bodies react to treatment. Medical professionals also perform studies by race, age, or nationality to see the effect of these characteristics on health.
Although this is attached to both the science and medical field, success in psychology would be impossible without the systematic study of human behavior, often analyzing results statistically.
Teachers are encouraged to be researchers in their classrooms, to see what teaching methods work on which students and understand why. They also should evaluate test items to determine if students are performing in a statistically expected way. At all levels of education and testing there are statistical reports about student performance, from kindergarten to an SAT or GRE.
Every large company employs its own statistical research divisions or firms to research issues related to products, employees, customer service, etc. Business success relies on knowing what is working and what isn't.
In many cases, basic statistical analysis can be done by using three main concepts: the mean, the median, and the mode.
The mean is the mathematical average. For example, a laundromat may conduct a study to see how many people use a machine each day, then calculate the average for each week.
The mean is the sum of the items divided by the number of items. In this case, we have seven items, so: mean = (105 + 50 + 40 + 50 + 70 + 80 + 95) / 7 = 70 people
The mode is the number that occurs most frequently in the data set. If we first organize the data in ascending order we get: 40, 50, 50, 70, 80, 95, 105. You can see 50 is the mode because it occurs twice while every other number occurs just once.
The median is found by organizing the data and then taking note of the number(s) that is in the middle. If we consider our data set again (40, 50, 50, 70, 80, 95, 105), you can see 70 is the number in the middle.
In data sets with an odd number of items, you simply select the middle item. In data sets with an even number of items, you must average the value of the two middle items to find the median.
Some of the main concerns with statistics are:
Data interpretation: Many people can interpret the same data differently. For example, if a report explains that 80% of high school students are left handed, it is easy to think that teenagers these days are mostly left handed. However, if you find that this is based on a population of students at Left Handed High, your opinion would change. When reading statistics, it is important to ask: what data was really captured and how was it interpreted?
Data validity?: Validity is a common term in the statistics world and it refers to whether the study is true or false. A study could be inaccurate, for example, if researchers pressured participants to answer a certain way. All factors must be representative of the real world to create a valid study.
Statistical studies are extremely important in our everyday life. Statistics are the method of conducting a study about a particular topic by collecting, organizing, interpreting, and finally presenting data.
Every human, at some level, is a statistician. We observe trends, sort out information, and then draw conclusions. This is similar to the actual process of gathering statistics, which begins with planning a study, which involves deciding what instruments to use, who to speak with, and how to analyze findings. Instruments are tools used in conducting a study like surveys, etc. From there, you collect data, when the instruments you selected are used, organize the data, putting the information together effectively to help expose patterns and other significant relationships. Interpret the data, valid assumptions supported by mathematical reasoning and finally, present the data, graphs, tables, and various diagrams are used to show relationships between data.
The mean, median and mode, the average, The middle-valued number(s), and the most common number, respectively are all calculated during the organization process, while validity, whether the study is true or false, is a common concern that is analyzed during the entire process.
Many major entities do more advanced and larger statistical analysis. Some major areas relying on statistics include government, education, science, and large companies. By doing more and better statistical analysis, we are able to understand the world around us, appreciate the value of analysis, and we are less deceived by numbers.
Statistics - the method of conducting a study about a particular topic by collecting, organizing, interpreting, and finally presenting data
Instruments - tools used in conducting a study like surveys, interviews, etc.
Mean - the mathematical average of a set of data
Mode - the number that occurs most frequently in the data set
Median - the middle number of an ordered data set
Validity - whether the study is true or false
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Back To CourseContemporary Math: Help and Review
20 chapters | 228 lessons